Solve 71/2-xgeq2/3

$$7 \frac { 1 } { 2 } - x \geq \frac { 2 } { 3 }$$

Solve for x

$$x\leq \frac{41}{6}$$

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.

$$3\left(7\times 2+1\right)-6x\geq 4$$

Multiply 7 and 2 to get 14.

$$3\left(14+1\right)-6x\geq 4$$

Add 14 and 1 to get 15.

$$3\times 15-6x\geq 4$$

Multiply 3 and 15 to get 45.

$$45-6x\geq 4$$

Subtract 45 from both sides.

$$-6x\geq 4-45$$

Subtract 45 from 4 to get -41.

$$-6x\geq -41$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x\leq \frac{-41}{-6}$$

Fraction \frac{-41}{-6} can be simplified to \frac{41}{6} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{41}{6}$$