Solve -x/4-4geq5x/3+1/6

$$- \frac { x } { 4 } - 4 \geq \frac { 5 x } { 3 } + \frac { 1 } { 6 }$$

Solve for x

$$x\leq -\frac{50}{23}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3,6. Since 12 is positive, the inequality direction remains the same.

$$-3x-48\geq 4\times 5x+2$$

Multiply 4 and 5 to get 20.

$$-3x-48\geq 20x+2$$

Subtract 20x from both sides.

$$-3x-48-20x\geq 2$$

Combine -3x and -20x to get -23x.

$$-23x-48\geq 2$$

Add 48 to both sides.

$$-23x\geq 2+48$$

Add 2 and 48 to get 50.

$$-23x\geq 50$$

Divide both sides by -23. Since -23 is negative, the inequality direction is changed.

$$x\leq -\frac{50}{23}$$