Solve -4x+3/2<-5(-2x-1)-1/4

$$- 4 x + \frac { 3 } { 2 } < - 5 ( - 2 x - 1 ) - \frac { 1 } { 4 }$$

Solve for x

$$x>-\frac{13}{56}$$

Solution Steps

Use the distributive property to multiply -5 by -2x-1.

$$-4x+\frac{3}{2}<10x+5-\frac{1}{4}$$

Convert 5 to fraction \frac{20}{4}.

$$-4x+\frac{3}{2}<10x+\frac{20}{4}-\frac{1}{4}$$

Since \frac{20}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$-4x+\frac{3}{2}<10x+\frac{20-1}{4}$$

Subtract 1 from 20 to get 19.

$$-4x+\frac{3}{2}<10x+\frac{19}{4}$$

Subtract 10x from both sides.

$$-4x+\frac{3}{2}-10x<\frac{19}{4}$$

Combine -4x and -10x to get -14x.

$$-14x+\frac{3}{2}<\frac{19}{4}$$

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

$$-14x<\frac{19}{4}-\frac{3}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{19}{4} and \frac{3}{2} to fractions with denominator 4.

$$-14x<\frac{19}{4}-\frac{6}{4}$$

Since \frac{19}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$-14x<\frac{19-6}{4}$$

Subtract 6 from 19 to get 13.

$$-14x<\frac{13}{4}$$

Divide both sides by -14. Since -14 is negative, the inequality direction is changed.

$$x>\frac{\frac{13}{4}}{-14}$$

Express \frac{\frac{13}{4}}{-14} as a single fraction.

$$x>\frac{13}{4\left(-14\right)}$$

Multiply 4 and -14 to get -56.

$$x>\frac{13}{-56}$$

Fraction \frac{13}{-56} can be rewritten as -\frac{13}{56} by extracting the negative sign.

$$x>-\frac{13}{56}$$