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

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

Solve for x

$$x = \frac{30}{19} = 1\frac{11}{19} \approx 1.578947368$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{4}{3} by 2x+3.

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

Express -\frac{4}{3}\times 2 as a single fraction.

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

Multiply -4 and 2 to get -8.

$$5x+\frac{-8}{3}x-\frac{4}{3}\times 3=2\left(3-2x\right)$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$5x-\frac{8}{3}x-\frac{4}{3}\times 3=2\left(3-2x\right)$$

Cancel out 3 and 3.

$$5x-\frac{8}{3}x-4=2\left(3-2x\right)$$

Combine 5x and -\frac{8}{3}x to get \frac{7}{3}x.

$$\frac{7}{3}x-4=2\left(3-2x\right)$$

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

$$\frac{7}{3}x-4=6-4x$$

Add 4x to both sides.

$$\frac{7}{3}x-4+4x=6$$

Combine \frac{7}{3}x and 4x to get \frac{19}{3}x.

$$\frac{19}{3}x-4=6$$

Add 4 to both sides.

$$\frac{19}{3}x=6+4$$

Add 6 and 4 to get 10.

$$\frac{19}{3}x=10$$

Multiply both sides by \frac{3}{19}, the reciprocal of \frac{19}{3}.

$$x=10\times \frac{3}{19}$$

Express 10\times \frac{3}{19} as a single fraction.

$$x=\frac{10\times 3}{19}$$

Multiply 10 and 3 to get 30.

$$x=\frac{30}{19}$$