Solve =(1+3x)=2/3(2-3x)

$$= ( 1 + 3 x ) = \frac { 2 } { 3 } ( 2 - 3 x )$$

Solve for x

$$x=\frac{1}{15}\approx 0.066666667$$

Steps for Solving Linear Equation

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

$$1+3x=\frac{2}{3}\times 2+\frac{2}{3}\left(-3\right)x$$

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

$$1+3x=\frac{2\times 2}{3}+\frac{2}{3}\left(-3\right)x$$

Multiply 2 and 2 to get 4.

$$1+3x=\frac{4}{3}+\frac{2}{3}\left(-3\right)x$$

Express \frac{2}{3}\left(-3\right) as a single fraction.

$$1+3x=\frac{4}{3}+\frac{2\left(-3\right)}{3}x$$

Multiply 2 and -3 to get -6.

$$1+3x=\frac{4}{3}+\frac{-6}{3}x$$

Divide -6 by 3 to get -2.

$$1+3x=\frac{4}{3}-2x$$

Add 2x to both sides.

$$1+3x+2x=\frac{4}{3}$$

Combine 3x and 2x to get 5x.

$$1+5x=\frac{4}{3}$$

Subtract 1 from both sides.

$$5x=\frac{4}{3}-1$$

Convert 1 to fraction \frac{3}{3}.

$$5x=\frac{4}{3}-\frac{3}{3}$$

Since \frac{4}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$5x=\frac{4-3}{3}$$

Subtract 3 from 4 to get 1.

$$5x=\frac{1}{3}$$

Divide both sides by 5.

$$x=\frac{\frac{1}{3}}{5}$$

Express \frac{\frac{1}{3}}{5} as a single fraction.

$$x=\frac{1}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$x=\frac{1}{15}$$