Solve 2x-2/3>-7/6

$$\frac { 2 x - 2 } { 3 } > - \frac { 7 } { 6 }$$

Solve for x

$$x>-\frac{3}{4}$$

Solution Steps

Multiply both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$2x-2>-\frac{7}{6}\times 3$$

Express -\frac{7}{6}\times 3 as a single fraction.

$$2x-2>\frac{-7\times 3}{6}$$

Multiply -7 and 3 to get -21.

$$2x-2>\frac{-21}{6}$$

Reduce the fraction \frac{-21}{6} to lowest terms by extracting and canceling out 3.

$$2x-2>-\frac{7}{2}$$

Add 2 to both sides.

$$2x>-\frac{7}{2}+2$$

Convert 2 to fraction \frac{4}{2}.

$$2x>-\frac{7}{2}+\frac{4}{2}$$

Since -\frac{7}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$2x>\frac{-7+4}{2}$$

Add -7 and 4 to get -3.

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

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

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

Express \frac{-\frac{3}{2}}{2} as a single fraction.

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

Multiply 2 and 2 to get 4.

$$x>\frac{-3}{4}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$x>-\frac{3}{4}$$