Solve x/3-8/7leq3x+2/3

$$\frac { x } { 3 } - \frac { 8 } { 7 } \leq 3 x + \frac { 2 } { 3 }$$

Solve for x

$$x\geq -\frac{19}{28}$$

Solution Steps

Multiply both sides of the equation by 21, the least common multiple of 3,7. Since 21 is positive, the inequality direction remains the same.

$$7x-24\leq 63x+14$$

Subtract 63x from both sides.

$$7x-24-63x\leq 14$$

Combine 7x and -63x to get -56x.

$$-56x-24\leq 14$$

Add 24 to both sides.

$$-56x\leq 14+24$$

Add 14 and 24 to get 38.

$$-56x\leq 38$$

Divide both sides by -56. Since -56 is negative, the inequality direction is changed.

$$x\geq \frac{38}{-56}$$

Reduce the fraction \frac{38}{-56} to lowest terms by extracting and canceling out 2.

$$x\geq -\frac{19}{28}$$