Solve x/7-6geqx

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

Solve for x

$$x\leq -7$$

Solution Steps

Subtract x from both sides.

$$\frac{x}{7}-6-x\geq 0$$

Combine \frac{x}{7} and -x to get -\frac{6}{7}x.

$$-\frac{6}{7}x-6\geq 0$$

Add 6 to both sides. Anything plus zero gives itself.

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

Multiply both sides by -\frac{7}{6}, the reciprocal of -\frac{6}{7}. Since -\frac{6}{7} is negative, the inequality direction is changed.

$$x\leq 6\left(-\frac{7}{6}\right)$$

Cancel out 6 and 6.

$$x\leq -7$$