Question

Complete each equation so that it is true for ALL values of x.

1/2(6x - 10) = ?
a) 3x - 5
b) 6x - 10
c) 12x - 20
d) 2x - 5

Answer 1

To make the equation 1/2(6x - 10) true for all x, multiply each term inside the parentheses by 1/2. This results in the equation 1/2(6x - 10) = 3x - 5, which corresponds to answer choice a) 3x - 5.

Step-by-step explanation:

To complete the equation 1/2(6x - 10) so that it is true for ALL values of x, we must distribute the 1/2 across the terms in parentheses. Therefore, 1/2 multiplied by 6x gives us 3x, and 1/2 multiplied by -10 gives us -5. The completed equation that will be true for all values of x is 1/2(6x - 10) = 3x - 5.

Here's the step-by-step explanation:

1. Multiply 6x by 1/2 to get 3x.
2. Multiply -10 by 1/2 to get -5.
3. Write down the equation: 1/2(6x - 10) = 3x - 5.

Checking the answer to see if it is reasonable:

• Option a) 3x - 5 is the correct simplification of 1/2(6x - 10).