Solve 3-x-1/4geq3(x+2)/8

$$3 - \frac { x - 1 } { 4 } \geq \frac { 3 ( x + 2 ) } { 8 }$$

Solve for x

$$x\leq 4$$

Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 4,8. Since 8 is positive, the inequality direction remains the same.

$$24-2\left(x-1\right)\geq 3\left(x+2\right)$$

Use the distributive property to multiply -2 by x-1.

$$24-2x+2\geq 3\left(x+2\right)$$

Add 24 and 2 to get 26.

$$26-2x\geq 3\left(x+2\right)$$

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

$$26-2x\geq 3x+6$$

Subtract 3x from both sides.

$$26-2x-3x\geq 6$$

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

$$26-5x\geq 6$$

Subtract 26 from both sides.

$$-5x\geq 6-26$$

Subtract 26 from 6 to get -20.

$$-5x\geq -20$$

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

$$x\leq \frac{-20}{-5}$$

Divide -20 by -5 to get 4.

$$x\leq 4$$