Question
To solve the equation: 24(34+x)=1,200
, give the reasons for each of the given steps.
What was done to the previous step to get to the current equation?
(1 point)
, give the reasons for each of the given steps.
What was done to the previous step to get to the current equation?
(1 point)
Answers
Answer
−4(2x+5) (1 point) Responses (−4−2x)+(−4−5) open paren negative 4 minus 2 x close paren plus open
Answer
Simplify: −4(2x+5)
(1 point)
Responses
(−4−2x)+(−4−5)
open paren negative 4 minus 2 x close paren plus open paren negative 4 minus 5 close paren
(−4÷2x)+(−4÷5)
open paren negative 4 divided by 2 x close paren plus open paren negative 4 divided by 5 close paren
(−4+2x)×(−4+5)
open paren negative 4 plus 2 x close paren times open paren negative 4 plus 5 close paren
(−4×2x)+(−4×5)
(1 point)
Responses
(−4−2x)+(−4−5)
open paren negative 4 minus 2 x close paren plus open paren negative 4 minus 5 close paren
(−4÷2x)+(−4÷5)
open paren negative 4 divided by 2 x close paren plus open paren negative 4 divided by 5 close paren
(−4+2x)×(−4+5)
open paren negative 4 plus 2 x close paren times open paren negative 4 plus 5 close paren
(−4×2x)+(−4×5)
Answer
Simplify: −4(2x+5)
(1 point)
Responses
A.(−4−2x)+(−4−5)
B. (−4÷2x)+(−4÷5)
C.(−4+2x)×(−4+5)
D. (−4×2x)+(−4×5)
(1 point)
Responses
A.(−4−2x)+(−4−5)
B. (−4÷2x)+(−4÷5)
C.(−4+2x)×(−4+5)
D. (−4×2x)+(−4×5)
Answer
Put the steps in order for solving the equation: −2(4x+8)+2x = −5x+10
(1 point)
(1 point)
Answer
A student solves the following problem: 2(x - 2) + 5x = 24
Step 1: 2x - 4 + 5x = 24
Step 2: 10x - 4 = 24
Step 3: 10x - 4 + 4 = 24 + 4
Step 4: 10x = 28
Step 5: 10x/10=28/10
Step 6: x = 2.8
Where is the mistake? What did the student do incorrectly?
Step 1: 2x - 4 + 5x = 24
Step 2: 10x - 4 = 24
Step 3: 10x - 4 + 4 = 24 + 4
Step 4: 10x = 28
Step 5: 10x/10=28/10
Step 6: x = 2.8
Where is the mistake? What did the student do incorrectly?
Answered by
GPT 3.5
The first step is to distribute the 24 to both terms inside the parentheses. This is done to simplify the expression by removing the parentheses and performing the multiplication.
The equation after distributing is: 816 + 24x = 1,200.
Next, we subtract 816 from both sides of the equation. This is done to isolate the term with the variable (24x) on one side of the equation.
The equation after subtracting 816 is: 24x = 384.
Finally, we divide both sides of the equation by 24 to solve for x. This is done to isolate the variable x and find its value.
The final equation after dividing by 24 is: x = 16.
Therefore, the previous step was dividing both sides of the equation by 24 to get to the current equation.
The equation after distributing is: 816 + 24x = 1,200.
Next, we subtract 816 from both sides of the equation. This is done to isolate the term with the variable (24x) on one side of the equation.
The equation after subtracting 816 is: 24x = 384.
Finally, we divide both sides of the equation by 24 to solve for x. This is done to isolate the variable x and find its value.
The final equation after dividing by 24 is: x = 16.
Therefore, the previous step was dividing both sides of the equation by 24 to get to the current equation.
Answered by
GPT 3.5
To solve the equation -4(2x+5), the first step is to distribute -4 to both terms inside the parentheses. This is done to simplify the expression by removing the parentheses and performing the multiplication.
-4(2x+5) becomes -8x - 20 after distributing.
Therefore, the previous step was distributing -4 to both terms inside the parentheses to get to the current equation.
-4(2x+5) becomes -8x - 20 after distributing.
Therefore, the previous step was distributing -4 to both terms inside the parentheses to get to the current equation.
Answered by
GPT 3.5
To simplify -4(2x+5), the first step is to distribute -4 to both terms inside the parentheses. This is done by multiplying -4 by each term inside the parentheses.
-4 multiplied by 2x gives -8x, and -4 multiplied by 5 gives -20.
Therefore, the simplified expression is -8x - 20.
The previous step was multiplying -4 by 2x and 5 to get -8x and -20, respectively.
-4 multiplied by 2x gives -8x, and -4 multiplied by 5 gives -20.
Therefore, the simplified expression is -8x - 20.
The previous step was multiplying -4 by 2x and 5 to get -8x and -20, respectively.
Answered by
GPT 3.5
To simplify -4(2x+5), we need to distribute -4 to both terms inside the parentheses.
This gives us: -4 * 2x + (-4) * 5
Simplifying further, -4 * 2x is -8x, and -4 * 5 is -20.
Therefore, the simplified expression is -8x - 20.
The correct response is D. (−4×2x)+(−4×5)
This gives us: -4 * 2x + (-4) * 5
Simplifying further, -4 * 2x is -8x, and -4 * 5 is -20.
Therefore, the simplified expression is -8x - 20.
The correct response is D. (−4×2x)+(−4×5)
Answered by
GPT 3.5
The correct order of steps for solving the equation −2(4x+8)+2x = −5x+10 is:
1. Distribute -2 to both terms inside the parentheses:
This gives us -8x - 16 + 2x = -5x + 10.
2. Combine like terms on both sides of the equation:
-8x + 2x - 16 = -5x + 10
3. Simplify the expression on the left side:
-6x - 16 = -5x + 10
4. Add 5x to both sides of the equation:
-6x - 16 + 5x = -5x + 5x + 10
5. Combine like terms on both sides:
-x - 16 = 10
6. Add 16 to both sides:
-x - 16 + 16 = 10 + 16
7. Simplify the expression on the left side:
-x = 26
8. Multiply both sides by -1:
(-1)(-x) = (-1)(26)
9. Simplify the expression on both sides:
x = -26.
Therefore, the steps in order for solving the equation −2(4x+8)+2x = −5x+10 are:
1. Distribute -2 to both terms inside the parentheses.
2. Combine like terms on both sides of the equation.
3. Simplify the expression on the left side.
4. Add 5x to both sides of the equation.
5. Combine like terms on both sides.
6. Add 16 to both sides.
7. Simplify the expression on the left side.
8. Multiply both sides by -1.
9. Simplify the expression on both sides.
The solution is x = -26.
1. Distribute -2 to both terms inside the parentheses:
This gives us -8x - 16 + 2x = -5x + 10.
2. Combine like terms on both sides of the equation:
-8x + 2x - 16 = -5x + 10
3. Simplify the expression on the left side:
-6x - 16 = -5x + 10
4. Add 5x to both sides of the equation:
-6x - 16 + 5x = -5x + 5x + 10
5. Combine like terms on both sides:
-x - 16 = 10
6. Add 16 to both sides:
-x - 16 + 16 = 10 + 16
7. Simplify the expression on the left side:
-x = 26
8. Multiply both sides by -1:
(-1)(-x) = (-1)(26)
9. Simplify the expression on both sides:
x = -26.
Therefore, the steps in order for solving the equation −2(4x+8)+2x = −5x+10 are:
1. Distribute -2 to both terms inside the parentheses.
2. Combine like terms on both sides of the equation.
3. Simplify the expression on the left side.
4. Add 5x to both sides of the equation.
5. Combine like terms on both sides.
6. Add 16 to both sides.
7. Simplify the expression on the left side.
8. Multiply both sides by -1.
9. Simplify the expression on both sides.
The solution is x = -26.
Answered by
GPT 3.5
The mistake made by the student is in Step 3. They incorrectly added 4 to both sides of the equation. However, when adding or subtracting to balance an equation, the operation should be done to both sides of the equation.
In this case, the correct step should be:
Step 3: 10x - 4 + 4 = 24 + 4
The mistake here is that the student added 4 to only one side of the equation, which creates an imbalance. The correct step should be:
Step 3: 10x - 4 + 4 = 24 + 4
Adding 4 to both sides of the equation ensures that the equation remains balanced and the result is correct.
The correct next step would be:
Step 3 (Correction): 10x = 28
In this case, the correct step should be:
Step 3: 10x - 4 + 4 = 24 + 4
The mistake here is that the student added 4 to only one side of the equation, which creates an imbalance. The correct step should be:
Step 3: 10x - 4 + 4 = 24 + 4
Adding 4 to both sides of the equation ensures that the equation remains balanced and the result is correct.
The correct next step would be:
Step 3 (Correction): 10x = 28
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