Question

Simplify, Isolate, Solve. What value of x makes the equation true? 5 – 2(3 – x) = 4x + 10

A. x = 1
B. x = 2
C. x = 3
D. x = 4

Answer 1

The value of x that makes the equation 5 – 2(3 – x) = 4x + 10 true is x = -5.5, which isn't one of the provided options, indicating a discrepancy in the provided choices or the equation itself.

Step-by-step explanation:

Step-by-Step Solution

To find the value of x that makes the equation 5 – 2(3 – x) = 4x + 10 true, you need to simplify and isolate the variable x following these steps:

1. Distribute -2 to both terms inside the parentheses: 5 - 2(3) + 2x = 4x + 10.
2. Simplify the left-hand side: 5 - 6 + 2x = 4x + 10.
3. Combine like terms: -1 + 2x = 4x + 10.
4. Move all x terms to one side: -1 = 2x + 10.
5. Subtract 10 from both sides: -11 = 2x.
6. Divide both sides by 2 to isolate x: x = -11 / 2.

So the value of x that satisfies the equation is x = -5.5, which is not one of the options provided (A. x = 1, B. x = 2, C. x = 3, D. x = 4). Therefore, there may be an error in the options given or in the original equation.

After solving, check the answer to see if it is reasonable by substituting x back into the original equation:

• 5 - 2(3 - (-5.5)) = 4(-5.5) + 10.
• 5 - 2(3 + 5.5) = -22 + 10.
• 5 - 2(8.5) = -12.
• 5 - 17 = -12, which confirms the answer is correct.