Solve x/5-1/6leqx/4+1

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

Solve for x

$$x\geq -\frac{70}{3}$$

Solution Steps

Multiply both sides of the equation by 60, the least common multiple of 5,6,4. Since 60 is positive, the inequality direction remains the same.

$$12x-10\leq 15x+60$$

Subtract 15x from both sides.

$$12x-10-15x\leq 60$$

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

$$-3x-10\leq 60$$

Add 10 to both sides.

$$-3x\leq 60+10$$

Add 60 and 10 to get 70.

$$-3x\leq 70$$

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

$$x\geq -\frac{70}{3}$$