7+2/3(3x+9)=23

Answer 1

To solve the equation \( 7 + \frac{2}{3}(3x + 9) = 23 \), let's start by isolating the term containing \( x \).

1. Subtract 7 from both sides: \[ \frac{2}{3}(3x + 9) = 23 - 7 \] \[ \frac{2}{3}(3x + 9) = 16 \]

2. Next, multiply both sides by \( \frac{3}{2} \) to eliminate the fraction: \[ 3x + 9 = 16 \cdot \frac{3}{2} \] Calculate \( 16 \cdot \frac{3}{2} \): \[ 16 \cdot \frac{3}{2} = 16 \cdot 1.5 = 24 \] So now we have: \[ 3x + 9 = 24 \]

3. Subtract 9 from both sides: \[ 3x = 24 - 9 \] \[ 3x = 15 \]

4. Finally, divide by 3: \[ x = \frac{15}{3} \] \[ x = 5 \]

Thus, the solution to the equation is \( x = 5 \).