Solve 3/2(x-1)geq2/3x-1/2

$$\frac { 3 } { 2 } ( x - 1 ) \geq \frac { 2 } { 3 } x - \frac { 1 } { 2 }$$

Solve for x

$$x\geq \frac{6}{5}$$

Solution Steps

Use the distributive property to multiply \frac{3}{2} by x-1.

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

Multiply \frac{3}{2} and -1 to get -\frac{3}{2}.

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

Subtract \frac{2}{3}x from both sides.

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

Combine \frac{3}{2}x and -\frac{2}{3}x to get \frac{5}{6}x.

$$\frac{5}{6}x-\frac{3}{2}\geq -\frac{1}{2}$$

Add \frac{3}{2} to both sides.

$$\frac{5}{6}x\geq -\frac{1}{2}+\frac{3}{2}$$

Since -\frac{1}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}x\geq \frac{-1+3}{2}$$

Add -1 and 3 to get 2.

$$\frac{5}{6}x\geq \frac{2}{2}$$

Divide 2 by 2 to get 1.

$$\frac{5}{6}x\geq 1$$

Multiply both sides by \frac{6}{5}, the reciprocal of \frac{5}{6}. Since \frac{5}{6} is positive, the inequality direction remains the same.

$$x\geq 1\times \frac{6}{5}$$

Multiply 1 and \frac{6}{5} to get \frac{6}{5}.

$$x\geq \frac{6}{5}$$