Solve 3(x+2)/4leq5x-7

$$\frac{ 3(x+2) }{ 4 } \leq 5x-7$$

Solve for x

$$x\geq 2$$

Solution Steps

Multiply both sides of the equation by 4. Since 4 is positive, the inequality direction remains the same.

$$3\left(x+2\right)\leq 20x-28$$

Use the distributive property to multiply 3 by x+2.

$$3x+6\leq 20x-28$$

Subtract 20x from both sides.

$$3x+6-20x\leq -28$$

Combine 3x and -20x to get -17x.

$$-17x+6\leq -28$$

Subtract 6 from both sides.

$$-17x\leq -28-6$$

Subtract 6 from -28 to get -34.

$$-17x\leq -34$$

Divide both sides by -17. Since -17 is negative, the inequality direction is changed.

$$x\geq \frac{-34}{-17}$$

Divide -34 by -17 to get 2.

$$x\geq 2$$