Solve 1-x/3leqx+7/2

$$1 - \frac { x } { 3 } \leq \frac { x + 7 } { 2 }$$

Solve for x

$$x\geq -3$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$6-2x\leq 3\left(x+7\right)$$

Use the distributive property to multiply 3 by x+7.

$$6-2x\leq 3x+21$$

Subtract 3x from both sides.

$$6-2x-3x\leq 21$$

Combine -2x and -3x to get -5x.

$$6-5x\leq 21$$

Subtract 6 from both sides.

$$-5x\leq 21-6$$

Subtract 6 from 21 to get 15.

$$-5x\leq 15$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq \frac{15}{-5}$$

Divide 15 by -5 to get -3.

$$x\geq -3$$