Solve 5-x/2-x-17/4geq7x-3/12

$$\frac { 5 - x } { 2 } - \frac { x - 17 } { 4 } \geq \frac { 7 x - 3 } { 12 }$$

Solve for x

$$x\leq \frac{21}{4}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 2,4,12. Since 12 is positive, the inequality direction remains the same.

$$6\left(5-x\right)-3\left(x-17\right)\geq 7x-3$$

Use the distributive property to multiply 6 by 5-x.

$$30-6x-3\left(x-17\right)\geq 7x-3$$

Use the distributive property to multiply -3 by x-17.

$$30-6x-3x+51\geq 7x-3$$

Combine -6x and -3x to get -9x.

$$30-9x+51\geq 7x-3$$

Add 30 and 51 to get 81.

$$81-9x\geq 7x-3$$

Subtract 7x from both sides.

$$81-9x-7x\geq -3$$

Combine -9x and -7x to get -16x.

$$81-16x\geq -3$$

Subtract 81 from both sides.

$$-16x\geq -3-81$$

Subtract 81 from -3 to get -84.

$$-16x\geq -84$$

Divide both sides by -16. Since -16 is negative, the inequality direction is changed.

$$x\leq \frac{-84}{-16}$$

Reduce the fraction \frac{-84}{-16} to lowest terms by extracting and canceling out -4.

$$x\leq \frac{21}{4}$$