Solve -3x+1/4leq-6+2x?

$$- 3 x + \frac { 1 } { 4 } \leq - 6 + 2 x ?$$

Solve for x

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

Solution Steps

Subtract 2x from both sides.

$$-3x+\frac{1}{4}-2x\leq -6$$

Combine -3x and -2x to get -5x.

$$-5x+\frac{1}{4}\leq -6$$

Subtract \frac{1}{4} from both sides.

$$-5x\leq -6-\frac{1}{4}$$

Convert -6 to fraction -\frac{24}{4}.

$$-5x\leq -\frac{24}{4}-\frac{1}{4}$$

Since -\frac{24}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$-5x\leq \frac{-24-1}{4}$$

Subtract 1 from -24 to get -25.

$$-5x\leq -\frac{25}{4}$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq \frac{-\frac{25}{4}}{-5}$$

Express \frac{-\frac{25}{4}}{-5} as a single fraction.

$$x\geq \frac{-25}{4\left(-5\right)}$$

Multiply 4 and -5 to get -20.

$$x\geq \frac{-25}{-20}$$

Reduce the fraction \frac{-25}{-20} to lowest terms by extracting and canceling out -5.

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