Solve 2/5x-2/9(x+2)=4

$$\frac { 2 } { 5 } x - \frac { 2 } { 9 } ( x + 2 ) = 4$$

Solve for x

$$x=25$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{2}{9} by x+2.

$$\frac{2}{5}x-\frac{2}{9}x-\frac{2}{9}\times 2=4$$

Express -\frac{2}{9}\times 2 as a single fraction.

$$\frac{2}{5}x-\frac{2}{9}x+\frac{-2\times 2}{9}=4$$

Multiply -2 and 2 to get -4.

$$\frac{2}{5}x-\frac{2}{9}x+\frac{-4}{9}=4$$

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$\frac{2}{5}x-\frac{2}{9}x-\frac{4}{9}=4$$

Combine \frac{2}{5}x and -\frac{2}{9}x to get \frac{8}{45}x.

$$\frac{8}{45}x-\frac{4}{9}=4$$

Add \frac{4}{9} to both sides.

$$\frac{8}{45}x=4+\frac{4}{9}$$

Convert 4 to fraction \frac{36}{9}.

$$\frac{8}{45}x=\frac{36}{9}+\frac{4}{9}$$

Since \frac{36}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\frac{8}{45}x=\frac{36+4}{9}$$

Add 36 and 4 to get 40.

$$\frac{8}{45}x=\frac{40}{9}$$

Multiply both sides by \frac{45}{8}, the reciprocal of \frac{8}{45}.

$$x=\frac{40}{9}\times \frac{45}{8}$$

Multiply \frac{40}{9} times \frac{45}{8} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{40\times 45}{9\times 8}$$

Do the multiplications in the fraction \frac{40\times 45}{9\times 8}.

$$x=\frac{1800}{72}$$

Divide 1800 by 72 to get 25.

$$x=25$$