Solve for me

Step 1: Distribute the fractions on both sides of the equation. $\frac{2}{3}x + \frac{2}{3}(5) = \frac{1}{2}x + \frac{1}{2}(7)$ $\frac{2}{3}x + \frac{10}{3} = \frac{1}{2}x + \frac{7}{2}$

Step 2: Find the least common multiple (LCM) of the denominators (3 and 2), which is 6. Multiply every term by 6 to eliminate the denominators. $6 \left(\frac{2}{3}x\right) + 6 \left(\frac{10}{3}\right) = 6 \left(\frac{1}{2}x\right) + 6 \left(\frac{7}{2}\right)$ $4x + 20 = 3x + 21$

Step 3: Subtract $3x$ from both sides of the equation. $4x - 3x + 20 = 3x - 3x + 21$ $x + 20 = 21$

Step 4: Subtract 20 from both sides of the equation. $x + 20 - 20 = 21 - 20$ $x = 1$

The solution is: $x = 1$