Solve x-3/2(2x-1)leq4

$$x - \frac { 3 } { 2 } ( 2 x - 1 ) \leq 4$$

Solve for x

$$x\geq -\frac{5}{4}$$

Solution Steps

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

$$x-\frac{3}{2}\times 2x-\frac{3}{2}\left(-1\right)\leq 4$$

Cancel out 2 and 2.

$$x-3x-\frac{3}{2}\left(-1\right)\leq 4$$

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

$$x-3x+\frac{3}{2}\leq 4$$

Combine x and -3x to get -2x.

$$-2x+\frac{3}{2}\leq 4$$

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

$$-2x\leq 4-\frac{3}{2}$$

Convert 4 to fraction \frac{8}{2}.

$$-2x\leq \frac{8}{2}-\frac{3}{2}$$

Since \frac{8}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$-2x\leq \frac{8-3}{2}$$

Subtract 3 from 8 to get 5.

$$-2x\leq \frac{5}{2}$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

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

Express \frac{\frac{5}{2}}{-2} as a single fraction.

$$x\geq \frac{5}{2\left(-2\right)}$$

Multiply 2 and -2 to get -4.

$$x\geq \frac{5}{-4}$$

Fraction \frac{5}{-4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$x\geq -\frac{5}{4}$$