Solve (-x+6/2leq2x+1/3

$$\frac { ( - x + 6 } { 2 } \leq \frac { 2 x + 1 } { 3 }$$

Solve for x

$$x\geq \frac{16}{7}$$

Solution Steps

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

$$3\left(-x+6\right)\leq 2\left(2x+1\right)$$

Use the distributive property to multiply 3 by -x+6.

$$3\left(-x\right)+18\leq 2\left(2x+1\right)$$

Use the distributive property to multiply 2 by 2x+1.

$$3\left(-x\right)+18\leq 4x+2$$

Subtract 4x from both sides.

$$3\left(-x\right)+18-4x\leq 2$$

Subtract 18 from both sides.

$$3\left(-x\right)-4x\leq 2-18$$

Subtract 18 from 2 to get -16.

$$3\left(-x\right)-4x\leq -16$$

Multiply 3 and -1 to get -3.

$$-3x-4x\leq -16$$

Combine -3x and -4x to get -7x.

$$-7x\leq -16$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x\geq \frac{-16}{-7}$$

Fraction \frac{-16}{-7} can be simplified to \frac{16}{7} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{16}{7}$$