Step 1: Distribute -6 to the terms inside the parentheses:
-6x - 18 + 4x = -6x + 30
Step 2: Combine like terms on each side of the equation:
-2x -18 = -6x + 30
Step 3: Move all the x terms to one side by adding 6x to both sides:
4x - 18 = 30
Step 4: Move all the constant terms to the other side by adding 18 to both sides:
4x - 18 + 18 = 30 + 18
Final Answer: 4x = 48
Order the the steps to solve the equation for x. Make sure to put the steps in order. Not all steps will be used.
-6(x + 3) + 4x = -6x + 30
Step 1 Step 2 Step 3 Step 4 Final Answer
x = 12
-6x -18 + 4x = -6 x + 30
-6x +3 + 4x = -6x + 30
4x - 18 = 30
-8x + 3 = 30
-2x -18 = -6x + 30
4x = 48
-8x = 27
x = -27/8
x = 12
-6x -18 + 4x = -6 x + 30
-6x +3 + 4x = -6x + 30
4x - 18 = 30
-8x + 3 = 30
-2x -18 = -6x + 30
4x = 48
-8x = 27
x = -27/8
21 answers
Solve the following equation for w.
6 - 3w = 2 - 4w + w
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No Solution
Infinitely Many Solutions
w = -4
w = 0
w = 2/3
6 - 3w = 2 - 4w + w
*
No Solution
Infinitely Many Solutions
w = -4
w = 0
w = 2/3
To solve the equation for w, we need to combine like terms and isolate the variable.
Step 1: Combine like terms on each side of the equation:
6 - 3w = 2 - 4w + w
Step 2: Combine the constant terms on each side:
6 - 3w = 2 - 3w
Step 3: Move all the w terms to one side by adding 3w to both sides:
6 = 2
Step 4: Since the equation simplifies to 6 = 2, which is not true, the equation has no solution.
Final Answer: No Solution
Step 1: Combine like terms on each side of the equation:
6 - 3w = 2 - 4w + w
Step 2: Combine the constant terms on each side:
6 - 3w = 2 - 3w
Step 3: Move all the w terms to one side by adding 3w to both sides:
6 = 2
Step 4: Since the equation simplifies to 6 = 2, which is not true, the equation has no solution.
Final Answer: No Solution
Tom and Jerry were at a State Fair. They each got a ticket for the Merry Go Round. Tom got a funnel cake, and Jerry got a churro. Tom had a certificate for $3 off the cost. Jerry paid the rest, which came to $12. Each Merry Go Round ticket was $5, and a funnel cake was $3.50. What equation represents this problem? What was the cost for a churro?
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5.00(2) +3.50 + x + 3.00 = 12.00; x = -4.50
5.00 + 3.50 + x - 3.00 = 12.00; x = 6.50
5.00(2) +3.50 + x - 3.00 = 12.00; x = 1.50
5.00 + 3.50 + x + 3 = 12.00; x = .50
*
5.00(2) +3.50 + x + 3.00 = 12.00; x = -4.50
5.00 + 3.50 + x - 3.00 = 12.00; x = 6.50
5.00(2) +3.50 + x - 3.00 = 12.00; x = 1.50
5.00 + 3.50 + x + 3 = 12.00; x = .50
Let's break down the problem and translate it into an equation.
Tom and Jerry each got a ticket for the Merry Go Round which cost $5 each. So, the total cost for the tickets would be $5 * 2 = $10.
Tom had a certificate for $3 off the cost, so we subtract $3 from the total cost:
$10 - $3 = $7
Tom also got a funnel cake which cost $3.50. So, we add $3.50 to the cost:
$7 + $3.50 = $10.50
Jerry paid the rest of the cost, which is $12. So, we subtract $10.50 from $12 to find the cost of the churro:
$12 - $10.50 = $1.50
Therefore, the equation representing this problem is:
5.00(2) + 3.50 + x - 3.00 = 12.00
where x represents the cost of the churro.
Final Answer: The cost for a churro is $1.50.
Tom and Jerry each got a ticket for the Merry Go Round which cost $5 each. So, the total cost for the tickets would be $5 * 2 = $10.
Tom had a certificate for $3 off the cost, so we subtract $3 from the total cost:
$10 - $3 = $7
Tom also got a funnel cake which cost $3.50. So, we add $3.50 to the cost:
$7 + $3.50 = $10.50
Jerry paid the rest of the cost, which is $12. So, we subtract $10.50 from $12 to find the cost of the churro:
$12 - $10.50 = $1.50
Therefore, the equation representing this problem is:
5.00(2) + 3.50 + x - 3.00 = 12.00
where x represents the cost of the churro.
Final Answer: The cost for a churro is $1.50.
Solve the following equation:
3(h + 2) - 4 = 11
3(h + 2) - 4 = 11
To solve the equation, we will follow the order of operations and isolate the variable h.
Step 1: Distribute the 3 to the terms inside the parentheses:
3h + 6 - 4 = 11
Step 2: Combine like terms:
3h + 2 = 11
Step 3: Move the constant term to the other side by subtracting 2 from both sides:
3h = 11 - 2
3h = 9
Step 4: Divide both sides by 3 to isolate the variable h:
h = 9/3
h = 3
Final Answer: The solution to the equation is h = 3.
Step 1: Distribute the 3 to the terms inside the parentheses:
3h + 6 - 4 = 11
Step 2: Combine like terms:
3h + 2 = 11
Step 3: Move the constant term to the other side by subtracting 2 from both sides:
3h = 11 - 2
3h = 9
Step 4: Divide both sides by 3 to isolate the variable h:
h = 9/3
h = 3
Final Answer: The solution to the equation is h = 3.
Solve the following equation.
5x + 2 = 5(x - 2) + 12
*
True
False
Open
5x + 2 = 5(x - 2) + 12
*
True
False
Open
To determine if the equation is true, false, or open, we need to simplify both sides of the equation and see if they are equal.
Let's simplify both sides of the equation:
Left side:
5x + 2
Right side:
5(x - 2) + 12
= 5x - 10 + 12
= 5x + 2
Now, we can see that both sides of the equation simplify to 5x + 2. Since they are equal, the equation is true.
Final Answer: True
Let's simplify both sides of the equation:
Left side:
5x + 2
Right side:
5(x - 2) + 12
= 5x - 10 + 12
= 5x + 2
Now, we can see that both sides of the equation simplify to 5x + 2. Since they are equal, the equation is true.
Final Answer: True
Which ordered pair is a solution of the equation? Choose all that apply.
y = 6x - 4
*
(0, 4)
(1, 2)
(-1, 10)
(2, 8)
(-2, -16)
(-1, -10)
y = 6x - 4
*
(0, 4)
(1, 2)
(-1, 10)
(2, 8)
(-2, -16)
(-1, -10)
To determine which ordered pairs are solutions of the equation, we substitute the x and y values into the equation and check if the equation holds true for each pair.
Let's check each ordered pair:
1. (0, 4):
y = 6x - 4
4 = 6(0) - 4
4 = -4
This equation is not true, so (0, 4) is not a solution.
2. (1, 2):
y = 6x - 4
2 = 6(1) - 4
2 = 6 - 4
2 = 2
This equation is true, so (1, 2) is a solution.
3. (-1, 10):
y = 6x - 4
10 = 6(-1) - 4
10 = -6 - 4
10 = -10
This equation is not true, so (-1, 10) is not a solution.
4. (2, 8):
y = 6x - 4
8 = 6(2) - 4
8 = 12 - 4
8 = 8
This equation is true, so (2, 8) is a solution.
5. (-2, -16):
y = 6x - 4
-16 = 6(-2) - 4
-16 = -12 - 4
-16 = -16
This equation is true, so (-2, -16) is a solution.
6. (-1, -10):
y = 6x - 4
-10 = 6(-1) - 4
-10 = -6 - 4
-10 = -10
This equation is true, so (-1, -10) is a solution.
From the checks above, the ordered pairs that are solutions of the equation are:
(1, 2), (2, 8), (-2, -16), and (-1, -10).
Final Answer: (1, 2), (2, 8), (-2, -16), and (-1, -10)
Let's check each ordered pair:
1. (0, 4):
y = 6x - 4
4 = 6(0) - 4
4 = -4
This equation is not true, so (0, 4) is not a solution.
2. (1, 2):
y = 6x - 4
2 = 6(1) - 4
2 = 6 - 4
2 = 2
This equation is true, so (1, 2) is a solution.
3. (-1, 10):
y = 6x - 4
10 = 6(-1) - 4
10 = -6 - 4
10 = -10
This equation is not true, so (-1, 10) is not a solution.
4. (2, 8):
y = 6x - 4
8 = 6(2) - 4
8 = 12 - 4
8 = 8
This equation is true, so (2, 8) is a solution.
5. (-2, -16):
y = 6x - 4
-16 = 6(-2) - 4
-16 = -12 - 4
-16 = -16
This equation is true, so (-2, -16) is a solution.
6. (-1, -10):
y = 6x - 4
-10 = 6(-1) - 4
-10 = -6 - 4
-10 = -10
This equation is true, so (-1, -10) is a solution.
From the checks above, the ordered pairs that are solutions of the equation are:
(1, 2), (2, 8), (-2, -16), and (-1, -10).
Final Answer: (1, 2), (2, 8), (-2, -16), and (-1, -10)
Which step is missing when solving the equation for x?
8x + 4 = 6 - 2(x - 4)
8x + 4 = 6 - 2x + 8
10x + 4 = 14
10x = 10
x = 1
*
8x + 4 = 12x
8x + 4 = 14 - 2x
8x = -2x +10
-12 = -12x
8x + 4 = 6 - 2(x - 4)
8x + 4 = 6 - 2x + 8
10x + 4 = 14
10x = 10
x = 1
*
8x + 4 = 12x
8x + 4 = 14 - 2x
8x = -2x +10
-12 = -12x
The missing step when solving the equation for x is:
8x + 4 = 6 - 2(x - 4)
8x + 4 = 6 - 2x + 8 (expanding the parentheses in -2(x - 4))
10x + 4 = 14 (combining like terms on both sides)
10x = 10 (subtracting 4 from both sides)
x = 1 (dividing both sides by 10)
The missing step is subtracting 4 from both sides of the equation.
Final Answer: -12 = -12x (This step is not necessary or related to solving the given equation)
8x + 4 = 6 - 2(x - 4)
8x + 4 = 6 - 2x + 8 (expanding the parentheses in -2(x - 4))
10x + 4 = 14 (combining like terms on both sides)
10x = 10 (subtracting 4 from both sides)
x = 1 (dividing both sides by 10)
The missing step is subtracting 4 from both sides of the equation.
Final Answer: -12 = -12x (This step is not necessary or related to solving the given equation)
Which of the equations has one solution? Select all that apply.
*
-2(w +2) = -3 - 2w
8k + 38 = -3(-6 - 4k)
-4(x + 3) = -12 - 4x
36 - 7y = -7(y - 5)
*
-2(w +2) = -3 - 2w
8k + 38 = -3(-6 - 4k)
-4(x + 3) = -12 - 4x
36 - 7y = -7(y - 5)
To determine which equations have one solution, we need to simplify each equation and see if it leads to a single solution.
1. -2(w +2) = -3 - 2w:
Simplifying both sides gives: -2w - 4 = -3 - 2w
We can see that the variables cancel out, giving a true statement: -4 = -3
This equation is inconsistent and has no solution.
2. 8k + 38 = -3(-6 - 4k):
Simplifying both sides gives: 8k + 38 = 18 + 12k
Combining like terms gives: 38 = 18 + 4k
Subtracting 18 from both sides gives: 20 = 4k
Dividing both sides by 4 gives: 5 = k
This equation has one unique solution: k = 5.
3. -4(x + 3) = -12 - 4x:
Simplifying both sides gives: -4x - 12 = -12 - 4x
We can see that the variables cancel out, giving a true statement: -12 = -12
This equation is consistent and has infinitely many solutions.
4. 36 - 7y = -7(y - 5):
Simplifying both sides gives: 36 - 7y = -7y + 35
Adding 7y to both sides gives: 36 = 35
This equation is inconsistent and has no solution.
From the analysis above, the equation that has one solution is:
8k + 38 = -3(-6 - 4k),
where k = 5.
Final Answer: 8k + 38 = -3(-6 - 4k) has one solution.
1. -2(w +2) = -3 - 2w:
Simplifying both sides gives: -2w - 4 = -3 - 2w
We can see that the variables cancel out, giving a true statement: -4 = -3
This equation is inconsistent and has no solution.
2. 8k + 38 = -3(-6 - 4k):
Simplifying both sides gives: 8k + 38 = 18 + 12k
Combining like terms gives: 38 = 18 + 4k
Subtracting 18 from both sides gives: 20 = 4k
Dividing both sides by 4 gives: 5 = k
This equation has one unique solution: k = 5.
3. -4(x + 3) = -12 - 4x:
Simplifying both sides gives: -4x - 12 = -12 - 4x
We can see that the variables cancel out, giving a true statement: -12 = -12
This equation is consistent and has infinitely many solutions.
4. 36 - 7y = -7(y - 5):
Simplifying both sides gives: 36 - 7y = -7y + 35
Adding 7y to both sides gives: 36 = 35
This equation is inconsistent and has no solution.
From the analysis above, the equation that has one solution is:
8k + 38 = -3(-6 - 4k),
where k = 5.
Final Answer: 8k + 38 = -3(-6 - 4k) has one solution.
The freshman class raised funds for a school dance. It costs $5,000 to rent out the hall plus $20 per student for food and drinks. The freshman class raised $20,000. Write and solve an equation to determine how many students can attend the school dance.
Let's denote the number of students attending the school dance as "s".
According to the given information, the cost to rent out the hall is $5,000, and each student costs $20 for food and drinks. Therefore, the total cost of the dance would be $5,000 + $20 * s.
The freshman class raised a total of $20,000, so we can set up the equation:
$5,000 + $20 * s = $20,000
Now, let's solve the equation to find the value of "s".
Subtract $5,000 from both sides:
$20 * s = $20,000 - $5,000
$20 * s = $15,000
To isolate "s", divide both sides by $20:
s = $15,000 / $20
s = 750
Therefore, the equation that represents the problem is "s = 750", which means that 750 students can attend the school dance.
Final Answer: 750 students can attend the school dance.
According to the given information, the cost to rent out the hall is $5,000, and each student costs $20 for food and drinks. Therefore, the total cost of the dance would be $5,000 + $20 * s.
The freshman class raised a total of $20,000, so we can set up the equation:
$5,000 + $20 * s = $20,000
Now, let's solve the equation to find the value of "s".
Subtract $5,000 from both sides:
$20 * s = $20,000 - $5,000
$20 * s = $15,000
To isolate "s", divide both sides by $20:
s = $15,000 / $20
s = 750
Therefore, the equation that represents the problem is "s = 750", which means that 750 students can attend the school dance.
Final Answer: 750 students can attend the school dance.
10 + 2x = 4x - 3(x + 2)
To solve the equation, we will follow the order of operations and simplify both sides step by step.
10 + 2x = 4x - 3(x + 2)
First, distribute the -3 to the terms inside the parentheses on the right side of the equation:
10 + 2x = 4x - 3x - 6
Next, combine like terms on the right side of the equation:
10 + 2x = x - 6
Now, move all the x terms to the left side and constant terms to the right side:
2x - x = -6 - 10
x = -16
The solution to the equation is x = -16.
Final Answer: x = -16
10 + 2x = 4x - 3(x + 2)
First, distribute the -3 to the terms inside the parentheses on the right side of the equation:
10 + 2x = 4x - 3x - 6
Next, combine like terms on the right side of the equation:
10 + 2x = x - 6
Now, move all the x terms to the left side and constant terms to the right side:
2x - x = -6 - 10
x = -16
The solution to the equation is x = -16.
Final Answer: x = -16
Error Analysis
Students were asked to solve the equation for m. Their work is shown below. Which student solved the equation correctly? Why did the other 2 students solve the equation incorrectly?
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Captionless Image
Students were asked to solve the equation for m. Their work is shown below. Which student solved the equation correctly? Why did the other 2 students solve the equation incorrectly?
*
Captionless Image
Without the specific work shown by the students, it is not possible to identify which student solved the equation correctly or identify the errors made by the other two students. Please provide the specific work shown by the students in order to analyze their solutions and identify any errors.