First, distribute the -2 to both terms inside the parentheses:
-2*4 - 2*n = 24
Then, simplify:
-8 - 2n = 24
Next, add 8 to both sides:
-2n = 32
Finally, divide both sides by -2:
n = -16
Solve for n.
−2(4+n)=24
13 answers
Solve for x.
5/8(x+1/2)=100
5/8(x+1/2)=100
To solve for x in the equation 5/8(x+1/2) = 100, we need to isolate the variable x.
Step 1: Distribute 5/8 to both terms inside the parentheses.
(5/8) * (x) + (5/8) * (1/2) = 100
Simplifying the left side:
(5/8)x + 5/16 = 100
Step 2: Move 5/16 to the right side of the equation by subtracting 5/16 from both sides.
(5/8)x = 100 - 5/16
Simplifying:
(5/8)x = 1600/16 - 5/16
(5/8)x = 1595/16
Step 3: Multiply both sides of the equation by the reciprocal of 5/8, which is 8/5.
(8/5) * (5/8)x = (8/5) * (1595/16)
Simplifying:
x = (1595/16) * (8/5)
x = 12760/80
x = 159.5
Therefore, the value of x that solves the equation 5/8(x+1/2) = 100 is x = 159.5.
Step 1: Distribute 5/8 to both terms inside the parentheses.
(5/8) * (x) + (5/8) * (1/2) = 100
Simplifying the left side:
(5/8)x + 5/16 = 100
Step 2: Move 5/16 to the right side of the equation by subtracting 5/16 from both sides.
(5/8)x = 100 - 5/16
Simplifying:
(5/8)x = 1600/16 - 5/16
(5/8)x = 1595/16
Step 3: Multiply both sides of the equation by the reciprocal of 5/8, which is 8/5.
(8/5) * (5/8)x = (8/5) * (1595/16)
Simplifying:
x = (1595/16) * (8/5)
x = 12760/80
x = 159.5
Therefore, the value of x that solves the equation 5/8(x+1/2) = 100 is x = 159.5.
Solve for w.
0.7(w+1.2)=2.1
0.7(w+1.2)=2.1
To solve for w in the equation 0.7(w+1.2) = 2.1, we need to isolate the variable w.
Step 1: Distribute 0.7 to both terms inside the parentheses.
0.7w + 0.7(1.2) = 2.1
Simplifying the left side:
0.7w + 0.84 = 2.1
Step 2: Move 0.84 to the right side of the equation by subtracting 0.84 from both sides.
0.7w = 2.1 - 0.84
Simplifying:
0.7w = 1.26
Step 3: Divide both sides of the equation by 0.7 to solve for w.
(0.7w) / 0.7 = 1.26 / 0.7
Simplifying:
w = 1.8
Therefore, the value of w that solves the equation 0.7(w+1.2) = 2.1 is w = 1.8.
Step 1: Distribute 0.7 to both terms inside the parentheses.
0.7w + 0.7(1.2) = 2.1
Simplifying the left side:
0.7w + 0.84 = 2.1
Step 2: Move 0.84 to the right side of the equation by subtracting 0.84 from both sides.
0.7w = 2.1 - 0.84
Simplifying:
0.7w = 1.26
Step 3: Divide both sides of the equation by 0.7 to solve for w.
(0.7w) / 0.7 = 1.26 / 0.7
Simplifying:
w = 1.8
Therefore, the value of w that solves the equation 0.7(w+1.2) = 2.1 is w = 1.8.
Solve for s.
−30(s−10)=−180
−30(s−10)=−180
To solve for s in the equation −30(s−10)=−180, we need to isolate the variable s.
Step 1: Distribute -30 to both terms inside the parentheses.
-30 * s + 30 * 10 = -180
Simplifying the left side:
-30s + 300 = -180
Step 2: Move 300 to the right side of the equation by subtracting 300 from both sides.
-30s = -180 - 300
Simplifying:
-30s = -480
Step 3: Divide both sides of the equation by -30 to solve for s.
(-30s) / -30 = -480 / -30
Simplifying:
s = 16
Therefore, the value of s that solves the equation −30(s−10) = −180 is s = 16.
Step 1: Distribute -30 to both terms inside the parentheses.
-30 * s + 30 * 10 = -180
Simplifying the left side:
-30s + 300 = -180
Step 2: Move 300 to the right side of the equation by subtracting 300 from both sides.
-30s = -180 - 300
Simplifying:
-30s = -480
Step 3: Divide both sides of the equation by -30 to solve for s.
(-30s) / -30 = -480 / -30
Simplifying:
s = 16
Therefore, the value of s that solves the equation −30(s−10) = −180 is s = 16.
Half the sum of a number and 10 is 8. Find the number.(1 point)
Responses
3
3
6
6
2
2
-2
Responses
3
3
6
6
2
2
-2
To solve the equation, "Half the sum of a number and 10 is 8," we can set up the equation:
(1/2)(x+10) = 8
Multiplying both sides of the equation by 2 to eliminate the fraction:
x + 10 = 16
Subtracting 10 from both sides of the equation:
x = 6
Therefore, the number that satisfies the equation is x = 6.
(1/2)(x+10) = 8
Multiplying both sides of the equation by 2 to eliminate the fraction:
x + 10 = 16
Subtracting 10 from both sides of the equation:
x = 6
Therefore, the number that satisfies the equation is x = 6.
John buys 8 packs of cookies at the grocery store. The cookies are on sale for 50 cents off per pack. He spends $20. Which equation can be used to find the original cost of a box of cookies, c?(1 point)
Responses
8(c+0.50)=208 times open paren c plus 0 point 5 0 close paren is equal to 20
8c−0.50=208 c minus 0 point 5 0 is equal to 20
8(c−0.50)=208 times open paren c minus 0 point 5 0 close paren is equal to 20
8−0.50c=208 minus 0 point 5 0 c is equal to 20
Responses
8(c+0.50)=208 times open paren c plus 0 point 5 0 close paren is equal to 20
8c−0.50=208 c minus 0 point 5 0 is equal to 20
8(c−0.50)=208 times open paren c minus 0 point 5 0 close paren is equal to 20
8−0.50c=208 minus 0 point 5 0 c is equal to 20
The correct equation that can be used to find the original cost of a box of cookies, c, is:
8(c-0.50) = 20
This equation takes into account that John bought 8 packs of cookies with a discount of 50 cents off per pack, and the total amount he spent was $20.
8(c-0.50) = 20
This equation takes into account that John bought 8 packs of cookies with a discount of 50 cents off per pack, and the total amount he spent was $20.
Consider this equation:
4(3x−2)=−24
Part 1. What is your first step in solving this equation? Remember, there is more than one way to solve this equation.
Part 2. How would you isolate the variable and solve for x after you have completed Part 1?
You do not need to solve the problem. Simply, describe your process.
**Please label Part 1 and Part 2 in your answer.**
4(3x−2)=−24
Part 1. What is your first step in solving this equation? Remember, there is more than one way to solve this equation.
Part 2. How would you isolate the variable and solve for x after you have completed Part 1?
You do not need to solve the problem. Simply, describe your process.
**Please label Part 1 and Part 2 in your answer.**
Part 1: The first step in solving the equation 4(3x - 2) = -24 can be to distribute the 4 to both terms inside the parentheses. This step is also known as applying the distributive property.
Part 2: After distributing the 4, we would have 12x - 8 = -24. To isolate the variable x, we can add 8 to both sides of the equation to eliminate the constant term (-8) on the left side. This would give us 12x = -16. Finally, to solve for x, we divide both sides of the equation by 12 to get the value of x.
So, my process to solve this equation would involve distributing the 4 in Part 1 and then isolating and solving for x in Part 2.
Part 2: After distributing the 4, we would have 12x - 8 = -24. To isolate the variable x, we can add 8 to both sides of the equation to eliminate the constant term (-8) on the left side. This would give us 12x = -16. Finally, to solve for x, we divide both sides of the equation by 12 to get the value of x.
So, my process to solve this equation would involve distributing the 4 in Part 1 and then isolating and solving for x in Part 2.
1 answer