Solve x+2/7geqx-3/2

$$\frac { x + 2 } { 7 } \geq \frac { x - 3 } { 2 }$$

Solve for x

$$x\leq 5$$

Solution Steps

Multiply both sides of the equation by 14, the least common multiple of 7,2. Since 14 is positive, the inequality direction remains the same.

$$2\left(x+2\right)\geq 7\left(x-3\right)$$

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

$$2x+4\geq 7\left(x-3\right)$$

Use the distributive property to multiply 7 by x-3.

$$2x+4\geq 7x-21$$

Subtract 7x from both sides.

$$2x+4-7x\geq -21$$

Combine 2x and -7x to get -5x.

$$-5x+4\geq -21$$

Subtract 4 from both sides.

$$-5x\geq -21-4$$

Subtract 4 from -21 to get -25.

$$-5x\geq -25$$

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

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

Divide -25 by -5 to get 5.

$$x\leq 5$$