Solve 25-x/2-x-17/4geqx/3-7x-3/12

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

Solve for x

$$x\leq 9$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 2,4,3,12. Since 12 is positive, the inequality direction remains the same.

$$12\left(5-x\right)-3\left(x-17\right)\geq 4x-\left(7x-3\right)$$

Use the distributive property to multiply 12 by 5-x.

$$60-12x-3\left(x-17\right)\geq 4x-\left(7x-3\right)$$

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

$$60-12x-3x+51\geq 4x-\left(7x-3\right)$$

Combine -12x and -3x to get -15x.

$$60-15x+51\geq 4x-\left(7x-3\right)$$

Add 60 and 51 to get 111.

$$111-15x\geq 4x-\left(7x-3\right)$$

To find the opposite of 7x-3, find the opposite of each term.

$$111-15x\geq 4x-7x-\left(-3\right)$$

The opposite of -3 is 3.

$$111-15x\geq 4x-7x+3$$

Combine 4x and -7x to get -3x.

$$111-15x\geq -3x+3$$

Add 3x to both sides.

$$111-15x+3x\geq 3$$

Combine -15x and 3x to get -12x.

$$111-12x\geq 3$$

Subtract 111 from both sides.

$$-12x\geq 3-111$$

Subtract 111 from 3 to get -108.

$$-12x\geq -108$$

Divide both sides by -12. Since -12 is negative, the inequality direction is changed.

$$x\leq \frac{-108}{-12}$$

Divide -108 by -12 to get 9.

$$x\leq 9$$