Solve 11-7/2xgeq61/2

$$11 - \frac { 7 } { 2 } x \geq 6 \frac { 1 } { 2 }$$

Solve for x

$$x\leq \frac{9}{7}$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$22-7x\geq 6\times 2+1$$

Multiply 6 and 2 to get 12.

$$22-7x\geq 12+1$$

Add 12 and 1 to get 13.

$$22-7x\geq 13$$

Subtract 22 from both sides.

$$-7x\geq 13-22$$

Subtract 22 from 13 to get -9.

$$-7x\geq -9$$

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

$$x\leq \frac{-9}{-7}$$

Fraction \frac{-9}{-7} can be simplified to \frac{9}{7} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{9}{7}$$