Question

solve the following equation for ( x ):
( \frac{2}{3}x - 2 = 10 )
( x = square )

Explanation:

Step1: Add 2 to both sides

To isolate the term with \( x \), we add 2 to both sides of the equation \(\frac{2}{3}x - 2 = 10\). This gives us \(\frac{2}{3}x - 2 + 2 = 10 + 2\), which simplifies to \(\frac{2}{3}x = 12\).

Step2: Multiply both sides by \(\frac{3}{2}\)

To solve for \( x \), we multiply both sides of the equation \(\frac{2}{3}x = 12\) by the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\). So we have \(x = 12\times\frac{3}{2}\). Calculating this, \(12\times\frac{3}{2} = \frac{12\times3}{2} = \frac{36}{2} = 18\).

Answer:

\( x = 18 \)