Solve x+1/4geq2x-16/5

$$\frac { x + 1 } { 4 } \geq \frac { 2 x - 16 } { 5 }$$

Solve for x

$$x\leq 23$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 4,5. Since 20 is positive, the inequality direction remains the same.

$$5\left(x+1\right)\geq 4\left(2x-16\right)$$

Use the distributive property to multiply 5 by x+1.

$$5x+5\geq 4\left(2x-16\right)$$

Use the distributive property to multiply 4 by 2x-16.

$$5x+5\geq 8x-64$$

Subtract 8x from both sides.

$$5x+5-8x\geq -64$$

Combine 5x and -8x to get -3x.

$$-3x+5\geq -64$$

Subtract 5 from both sides.

$$-3x\geq -64-5$$

Subtract 5 from -64 to get -69.

$$-3x\geq -69$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x\leq \frac{-69}{-3}$$

Divide -69 by -3 to get 23.

$$x\leq 23$$