Solve 4x+7/7-3x-8/5leq17/35

$$\frac { 4 x + 7 } { 7 } - \frac { 3 x - 8 } { 5 } \leq \frac { 17 } { 35 }$$

Solve for x

$$x\geq 74$$

Solution Steps

Multiply both sides of the equation by 35, the least common multiple of 7,5,35. Since 35 is positive, the inequality direction remains the same.

$$5\left(4x+7\right)-7\left(3x-8\right)\leq 17$$

Use the distributive property to multiply 5 by 4x+7.

$$20x+35-7\left(3x-8\right)\leq 17$$

Use the distributive property to multiply -7 by 3x-8.

$$20x+35-21x+56\leq 17$$

Combine 20x and -21x to get -x.

$$-x+35+56\leq 17$$

Add 35 and 56 to get 91.

$$-x+91\leq 17$$

Subtract 91 from both sides.

$$-x\leq 17-91$$

Subtract 91 from 17 to get -74.

$$-x\leq -74$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\geq \frac{-74}{-1}$$

Fraction \frac{-74}{-1} can be simplified to 74 by removing the negative sign from both the numerator and the denominator.

$$x\geq 74$$