Solve 9x-1<3/4(16x-2)

$$9 x - 1 < \frac { 3 } { 4 } ( 16 x - 2 )$$

Solve for x

$$x>\frac{1}{6}$$

Solution Steps

Use the distributive property to multiply \frac{3}{4} by 16x-2.

$$9x-1<\frac{3}{4}\times 16x+\frac{3}{4}\left(-2\right)$$

Express \frac{3}{4}\times 16 as a single fraction.

$$9x-1<\frac{3\times 16}{4}x+\frac{3}{4}\left(-2\right)$$

Multiply 3 and 16 to get 48.

$$9x-1<\frac{48}{4}x+\frac{3}{4}\left(-2\right)$$

Divide 48 by 4 to get 12.

$$9x-1<12x+\frac{3}{4}\left(-2\right)$$

Express \frac{3}{4}\left(-2\right) as a single fraction.

$$9x-1<12x+\frac{3\left(-2\right)}{4}$$

Multiply 3 and -2 to get -6.

$$9x-1<12x+\frac{-6}{4}$$

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

$$9x-1<12x-\frac{3}{2}$$

Subtract 12x from both sides.

$$9x-1-12x<-\frac{3}{2}$$

Combine 9x and -12x to get -3x.

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

Add 1 to both sides.

$$-3x<-\frac{3}{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$-3x<-\frac{3}{2}+\frac{2}{2}$$

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

$$-3x<\frac{-3+2}{2}$$

Add -3 and 2 to get -1.

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

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

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

Express \frac{-\frac{1}{2}}{-3} as a single fraction.

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

Multiply 2 and -3 to get -6.

$$x>\frac{-1}{-6}$$

Fraction \frac{-1}{-6} can be simplified to \frac{1}{6} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{1}{6}$$