Solve -3/4(1+2/3x)=-1/2

$$- \frac { 3 } { 4 } ( 1 + \frac { 2 } { 3 } x ) = - \frac { 1 } { 2 }$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Multiply both sides by -\frac{4}{3}, the reciprocal of -\frac{3}{4}.

$$1+\frac{2}{3}x=-\frac{1}{2}\left(-\frac{4}{3}\right)$$

Multiply -\frac{1}{2} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{2}{3}x=\frac{-\left(-4\right)}{2\times 3}$$

Do the multiplications in the fraction \frac{-\left(-4\right)}{2\times 3}.

$$1+\frac{2}{3}x=\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$1+\frac{2}{3}x=\frac{2}{3}$$

Subtract 1 from both sides.

$$\frac{2}{3}x=\frac{2}{3}-1$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{2}{3}x=\frac{2}{3}-\frac{3}{3}$$

Since \frac{2}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}x=\frac{2-3}{3}$$

Subtract 3 from 2 to get -1.

$$\frac{2}{3}x=-\frac{1}{3}$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$x=-\frac{1}{3}\times \frac{3}{2}$$

Multiply -\frac{1}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-3}{3\times 2}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{-1}{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$x=-\frac{1}{2}$$