Solve 6x-2>3(1/2x-3/2)

$$6 x - 2 > 3 ( \frac { 1 } { 2 } x - \frac { 3 } { 2 } )$$

Solve for x

$$x>-\frac{5}{9}$$

Solution Steps

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

$$6x-2>3\times \frac{1}{2}x+3\left(-\frac{3}{2}\right)$$

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

$$6x-2>\frac{3}{2}x+3\left(-\frac{3}{2}\right)$$

Express 3\left(-\frac{3}{2}\right) as a single fraction.

$$6x-2>\frac{3}{2}x+\frac{3\left(-3\right)}{2}$$

Multiply 3 and -3 to get -9.

$$6x-2>\frac{3}{2}x+\frac{-9}{2}$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$6x-2>\frac{3}{2}x-\frac{9}{2}$$

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

$$6x-2-\frac{3}{2}x>-\frac{9}{2}$$

Combine 6x and -\frac{3}{2}x to get \frac{9}{2}x.

$$\frac{9}{2}x-2>-\frac{9}{2}$$

Add 2 to both sides.

$$\frac{9}{2}x>-\frac{9}{2}+2$$

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

$$\frac{9}{2}x>-\frac{9}{2}+\frac{4}{2}$$

Since -\frac{9}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$\frac{9}{2}x>\frac{-9+4}{2}$$

Add -9 and 4 to get -5.

$$\frac{9}{2}x>-\frac{5}{2}$$

Multiply both sides by \frac{2}{9}, the reciprocal of \frac{9}{2}. Since \frac{9}{2} is positive, the inequality direction remains the same.

$$x>-\frac{5}{2}\times \frac{2}{9}$$

Multiply -\frac{5}{2} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{-5\times 2}{2\times 9}$$

Cancel out 2 in both numerator and denominator.

$$x>\frac{-5}{9}$$

Fraction \frac{-5}{9} can be rewritten as -\frac{5}{9} by extracting the negative sign.

$$x>-\frac{5}{9}$$