Solve 15+xgeq2/3(27+x)

$$15+x \geq \frac{ 2 }{ 3 } (27+x)$$

Solve for x

$$x\geq 9$$

Solution Steps

Use the distributive property to multiply \frac{2}{3} by 27+x.

$$15+x\geq \frac{2}{3}\times 27+\frac{2}{3}x$$

Express \frac{2}{3}\times 27 as a single fraction.

$$15+x\geq \frac{2\times 27}{3}+\frac{2}{3}x$$

Multiply 2 and 27 to get 54.

$$15+x\geq \frac{54}{3}+\frac{2}{3}x$$

Divide 54 by 3 to get 18.

$$15+x\geq 18+\frac{2}{3}x$$

Subtract \frac{2}{3}x from both sides.

$$15+x-\frac{2}{3}x\geq 18$$

Combine x and -\frac{2}{3}x to get \frac{1}{3}x.

$$15+\frac{1}{3}x\geq 18$$

Subtract 15 from both sides.

$$\frac{1}{3}x\geq 18-15$$

Subtract 15 from 18 to get 3.

$$\frac{1}{3}x\geq 3$$

Multiply both sides by 3, the reciprocal of \frac{1}{3}. Since \frac{1}{3} is positive, the inequality direction remains the same.

$$x\geq 3\times 3$$

Multiply 3 and 3 to get 9.

$$x\geq 9$$