Solve x-7+x/4-11x-8/12geqx-5/3

$$x - \frac { 7 + x } { 4 } - \frac { 11 x - 8 } { 12 } \geq \frac { x - 5 } { 3 }$$

Solve for x

$$x\leq \frac{7}{6}$$

Solution Steps

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

$$12x-3\left(7+x\right)-\left(11x-8\right)\geq 4\left(x-5\right)$$

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

$$12x-21-3x-\left(11x-8\right)\geq 4\left(x-5\right)$$

Combine 12x and -3x to get 9x.

$$9x-21-\left(11x-8\right)\geq 4\left(x-5\right)$$

To find the opposite of 11x-8, find the opposite of each term.

$$9x-21-11x-\left(-8\right)\geq 4\left(x-5\right)$$

The opposite of -8 is 8.

$$9x-21-11x+8\geq 4\left(x-5\right)$$

Combine 9x and -11x to get -2x.

$$-2x-21+8\geq 4\left(x-5\right)$$

Add -21 and 8 to get -13.

$$-2x-13\geq 4\left(x-5\right)$$

Use the distributive property to multiply 4 by x-5.

$$-2x-13\geq 4x-20$$

Subtract 4x from both sides.

$$-2x-13-4x\geq -20$$

Combine -2x and -4x to get -6x.

$$-6x-13\geq -20$$

Add 13 to both sides.

$$-6x\geq -20+13$$

Add -20 and 13 to get -7.

$$-6x\geq -7$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x\leq \frac{-7}{-6}$$

Fraction \frac{-7}{-6} can be simplified to \frac{7}{6} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{7}{6}$$