Solve 5/2+7xleq4x-7/2

$$\frac { 5 } { 2 } + 7 x \leq 4 x - \frac { 7 } { 2 }$$

Solve for x

$$x\leq -2$$

Solution Steps

Subtract 4x from both sides.

$$\frac{5}{2}+7x-4x\leq -\frac{7}{2}$$

Combine 7x and -4x to get 3x.

$$\frac{5}{2}+3x\leq -\frac{7}{2}$$

Subtract \frac{5}{2} from both sides.

$$3x\leq -\frac{7}{2}-\frac{5}{2}$$

Since -\frac{7}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$3x\leq \frac{-7-5}{2}$$

Subtract 5 from -7 to get -12.

$$3x\leq \frac{-12}{2}$$

Divide -12 by 2 to get -6.

$$3x\leq -6$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x\leq \frac{-6}{3}$$

Divide -6 by 3 to get -2.

$$x\leq -2$$