Solve 3(2-x)geq47

$$3 ( 2 - x ) \geq 47$$

Solve for x

$$x\leq -\frac{41}{3}$$

Solution Steps

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$2-x\geq \frac{47}{3}$$

Subtract 2 from both sides.

$$-x\geq \frac{47}{3}-2$$

Convert 2 to fraction \frac{6}{3}.

$$-x\geq \frac{47}{3}-\frac{6}{3}$$

Since \frac{47}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$-x\geq \frac{47-6}{3}$$

Subtract 6 from 47 to get 41.

$$-x\geq \frac{41}{3}$$

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

$$x\leq \frac{\frac{41}{3}}{-1}$$

Express \frac{\frac{41}{3}}{-1} as a single fraction.

$$x\leq \frac{41}{3\left(-1\right)}$$

Multiply 3 and -1 to get -3.

$$x\leq \frac{41}{-3}$$

Fraction \frac{41}{-3} can be rewritten as -\frac{41}{3} by extracting the negative sign.

$$x\leq -\frac{41}{3}$$