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

Answer 1

To solve the equation \( 7 + \frac{2}{3}(2x + 9) = 23 \), follow these steps:

1. Start by isolating the term with \( x \): \[ \frac{2}{3}(2x + 9) = 23 - 7 \] \[ \frac{2}{3}(2x + 9) = 16 \]

2. Next, eliminate the fraction by multiplying both sides by \( \frac{3}{2} \): \[ 2x + 9 = 16 \cdot \frac{3}{2} \] \[ 2x + 9 = 24 \]

3. Now, isolate \( 2x \) by subtracting 9 from both sides: \[ 2x = 24 - 9 \] \[ 2x = 15 \]

4. Finally, divide by 2 to find \( x \): \[ x = \frac{15}{2} = 7.5 \]

So, the solution is: \[ \boxed{7.5} \]