Solve 7(3-x)geq5

$$7 ( 3 - x ) \geq 5$$

Solve for x

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

Solution Steps

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$3-x\geq \frac{5}{7}$$

Subtract 3 from both sides.

$$-x\geq \frac{5}{7}-3$$

Convert 3 to fraction \frac{21}{7}.

$$-x\geq \frac{5}{7}-\frac{21}{7}$$

Since \frac{5}{7} and \frac{21}{7} have the same denominator, subtract them by subtracting their numerators.

$$-x\geq \frac{5-21}{7}$$

Subtract 21 from 5 to get -16.

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

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\leq \frac{-\frac{16}{7}}{-1}$$

Express \frac{-\frac{16}{7}}{-1} as a single fraction.

$$x\leq \frac{-16}{7\left(-1\right)}$$

Multiply 7 and -1 to get -7.

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

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

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