Final answer:
The value of x that makes the equation 3/4(x + 20) = 2 + (x - 2) true is 60 after distributing, combining like terms, and isolating x.
Step-by-step explanation:
Solving a Linear Equation
To find the value of x that makes the equation 3/4(x + 20) = 2 + (x - 2) true, we first distribute the 3/4 across the parentheses on the left side:
3/4 × x + 3/4 × 20 = 2 + (x - 2)
Which simplifies to:
(3/4)x + 15 = 2 + x - 2
Then, we combine like terms on the right side:
(3/4)x + 15 = x
Next, we move all terms containing x to one side of the equation:
(3/4)x - x = -15
This becomes:
-1/4x = -15
To isolate x, we divide both sides by -1/4:
x = -15 ÷ (-1/4)
x = 60
Therefore, the value of x that makes the equation true is 60.