Solve 2/3(2x+5)=2(3-4x)+16

$$\frac { 2 } { 3 } ( 2 x + 5 ) = 2 ( 3 - 4 x ) + 16$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by 2x+5.

$$\frac{2}{3}\times 2x+\frac{2}{3}\times 5=2\left(3-4x\right)+16$$

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

$$\frac{2\times 2}{3}x+\frac{2}{3}\times 5=2\left(3-4x\right)+16$$

Multiply 2 and 2 to get 4.

$$\frac{4}{3}x+\frac{2}{3}\times 5=2\left(3-4x\right)+16$$

Express \frac{2}{3}\times 5 as a single fraction.

$$\frac{4}{3}x+\frac{2\times 5}{3}=2\left(3-4x\right)+16$$

Multiply 2 and 5 to get 10.

$$\frac{4}{3}x+\frac{10}{3}=2\left(3-4x\right)+16$$

Use the distributive property to multiply 2 by 3-4x.

$$\frac{4}{3}x+\frac{10}{3}=6-8x+16$$

Add 6 and 16 to get 22.

$$\frac{4}{3}x+\frac{10}{3}=22-8x$$

Add 8x to both sides.

$$\frac{4}{3}x+\frac{10}{3}+8x=22$$

Combine \frac{4}{3}x and 8x to get \frac{28}{3}x.

$$\frac{28}{3}x+\frac{10}{3}=22$$

Subtract \frac{10}{3} from both sides.

$$\frac{28}{3}x=22-\frac{10}{3}$$

Convert 22 to fraction \frac{66}{3}.

$$\frac{28}{3}x=\frac{66}{3}-\frac{10}{3}$$

Since \frac{66}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28}{3}x=\frac{66-10}{3}$$

Subtract 10 from 66 to get 56.

$$\frac{28}{3}x=\frac{56}{3}$$

Multiply both sides by \frac{3}{28}, the reciprocal of \frac{28}{3}.

$$x=\frac{56}{3}\times \frac{3}{28}$$

Multiply \frac{56}{3} times \frac{3}{28} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{56\times 3}{3\times 28}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{56}{28}$$

Divide 56 by 28 to get 2.

$$x=2$$