To determine which value of [tex]\( x \)[/tex] makes the equation true, we need to solve the equation step by step.
Given the equation:
[tex]\[ -9x + 15 = 3(2 - x) \][/tex]
### Step 1: Distribute the 3 on the right side of the equation.
[tex]\[ -9x + 15 = 3 \cdot 2 + 3 \cdot (-x) \][/tex]
[tex]\[ -9x + 15 = 6 - 3x \][/tex]
### Step 2: Move all terms involving [tex]\( x \)[/tex] to one side of the equation and constants to the other side.
First, add [tex]\( 3x \)[/tex] to both sides to get rid of [tex]\( -3x \)[/tex] on the right side:
[tex]\[ -9x + 3x + 15 = 6 - 3x + 3x \][/tex]
[tex]\[ -6x + 15 = 6 \][/tex]
Next, subtract 15 from both sides to get rid of the constant on the left side:
[tex]\[ -6x + 15 - 15 = 6 - 15 \][/tex]
[tex]\[ -6x = -9 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex] by dividing both sides by -6.
[tex]\[ x = \frac{-9}{-6} \][/tex]
[tex]\[ x = \frac{3}{2} \][/tex]
### Verification:
Let’s verify by substituting [tex]\( x = \frac{3}{2} \)[/tex] back into the original equation:
[tex]\[ -9 \left( \frac{3}{2} \right) + 15 = 3 \left( 2 - \frac{3}{2} \right) \][/tex]
Calculate each side separately:
Left side:
[tex]\[ -9 \left( \frac{3}{2} \right) + 15 = -\frac{27}{2} + 15 = -\frac{27}{2} + \frac{30}{2} = \frac{3}{2} \][/tex]
Right side:
[tex]\[ 3 \left( 2 - \frac{3}{2} \right) = 3 \left( \frac{4}{2} - \frac{3}{2} \right) = 3 \left( \frac{1}{2} \right) = \frac{3}{2} \][/tex]
Both sides match, confirming our solution is correct.
Therefore, the value of [tex]\( x \)[/tex] that makes the equation true is:
[tex]\[ \boxed{\frac{3}{2}} \][/tex]
