Solve -3/4+4x/5geq11/8+x-5/8

$$- \frac { 3 } { 4 } + \frac { 4 x } { 5 } \geq \frac { 11 } { 8 } + x - \frac { 5 } { 8 }$$

Solve for x

$$x\leq -\frac{15}{2}$$

Solution Steps

Multiply both sides of the equation by 40, the least common multiple of 4,5,8. Since 40 is positive, the inequality direction remains the same.

$$-30+8\times 4x\geq 55+40x-25$$

Multiply 8 and 4 to get 32.

$$-30+32x\geq 55+40x-25$$

Subtract 25 from 55 to get 30.

$$-30+32x\geq 30+40x$$

Subtract 40x from both sides.

$$-30+32x-40x\geq 30$$

Combine 32x and -40x to get -8x.

$$-30-8x\geq 30$$

Add 30 to both sides.

$$-8x\geq 30+30$$

Add 30 and 30 to get 60.

$$-8x\geq 60$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$x\leq \frac{60}{-8}$$

Reduce the fraction \frac{60}{-8} to lowest terms by extracting and canceling out 4.

$$x\leq -\frac{15}{2}$$