Solve x-3x-8/2geq2(13-x)/7-1

$$x - \frac { 3 x - 8 } { 2 } \geq \frac { 2 ( 13 - x ) } { 7 } - 1$$

Solve for x

$$x\leq 6$$

Solution Steps

Multiply both sides of the equation by 14, the least common multiple of 2,7. Since 14 is positive, the inequality direction remains the same.

$$14x-7\left(3x-8\right)\geq 2\times 2\left(13-x\right)-14$$

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

$$14x-21x+56\geq 2\times 2\left(13-x\right)-14$$

Combine 14x and -21x to get -7x.

$$-7x+56\geq 2\times 2\left(13-x\right)-14$$

Multiply 2 and 2 to get 4.

$$-7x+56\geq 4\left(13-x\right)-14$$

Use the distributive property to multiply 4 by 13-x.

$$-7x+56\geq 52-4x-14$$

Subtract 14 from 52 to get 38.

$$-7x+56\geq 38-4x$$

Add 4x to both sides.

$$-7x+56+4x\geq 38$$

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

$$-3x+56\geq 38$$

Subtract 56 from both sides.

$$-3x\geq 38-56$$

Subtract 56 from 38 to get -18.

$$-3x\geq -18$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x\leq \frac{-18}{-3}$$

Divide -18 by -3 to get 6.

$$x\leq 6$$