Solve 150+x>2/3(270+x)

$$150+x > \frac{ 2 }{ 3 } (270+x)$$

Solve for x

$$x>90$$

Solution Steps

Use the distributive property to multiply \frac{2}{3} by 270+x.

$$150+x>\frac{2}{3}\times 270+\frac{2}{3}x$$

Express \frac{2}{3}\times 270 as a single fraction.

$$150+x>\frac{2\times 270}{3}+\frac{2}{3}x$$

Multiply 2 and 270 to get 540.

$$150+x>\frac{540}{3}+\frac{2}{3}x$$

Divide 540 by 3 to get 180.

$$150+x>180+\frac{2}{3}x$$

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

$$150+x-\frac{2}{3}x>180$$

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

$$150+\frac{1}{3}x>180$$

Subtract 150 from both sides.

$$\frac{1}{3}x>180-150$$

Subtract 150 from 180 to get 30.

$$\frac{1}{3}x>30$$

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

$$x>30\times 3$$

Multiply 30 and 3 to get 90.

$$x>90$$