Solve 1/3x-1/2xgeqx+1

$$\frac { 1 } { 3 } x - \frac { 1 } { 2 } x \geq x + 1$$

Solve for x

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

Solution Steps

Combine \frac{1}{3}x and -\frac{1}{2}x to get -\frac{1}{6}x.

$$-\frac{1}{6}x\geq x+1$$

Subtract x from both sides.

$$-\frac{1}{6}x-x\geq 1$$

Combine -\frac{1}{6}x and -x to get -\frac{7}{6}x.

$$-\frac{7}{6}x\geq 1$$

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

$$x\leq 1\left(-\frac{6}{7}\right)$$

Multiply 1 and -\frac{6}{7} to get -\frac{6}{7}.

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