Solve 0,4x-9/0.5-x-5/2=0.03+0.02x/0.03

$$\frac { 0,4 x - 9 } { 0.5 } - \frac { x - 5 } { 2 } = \frac { 0.03 + 0.02 x } { 0.03 }$$

Solve for x

$$x=-45$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\times \frac{0.4x-9}{0.5}-\left(x-5\right)=2\times \frac{0.03+0.02x}{0.03}$$

To find the opposite of x-5, find the opposite of each term.

$$2\times \frac{0.4x-9}{0.5}-x-\left(-5\right)=2\times \frac{0.03+0.02x}{0.03}$$

The opposite of -5 is 5.

$$2\times \frac{0.4x-9}{0.5}-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Divide each term of 0.4x-9 by 0.5 to get \frac{0.4x}{0.5}+\frac{-9}{0.5}.

$$2\left(\frac{0.4x}{0.5}+\frac{-9}{0.5}\right)-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Divide 0.4x by 0.5 to get 0.8x.

$$2\left(0.8x+\frac{-9}{0.5}\right)-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Expand \frac{-9}{0.5} by multiplying both numerator and the denominator by 10.

$$2\left(0.8x+\frac{-90}{5}\right)-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Divide -90 by 5 to get -18.

$$2\left(0.8x-18\right)-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Use the distributive property to multiply 2 by 0.8x-18.

$$1.6x-36-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Combine 1.6x and -x to get 0.6x.

$$0.6x-36+5=2\times \frac{0.03+0.02x}{0.03}$$

Add -36 and 5 to get -31.

$$0.6x-31=2\times \frac{0.03+0.02x}{0.03}$$

Divide each term of 0.03+0.02x by 0.03 to get \frac{0.03}{0.03}+\frac{0.02x}{0.03}.

$$0.6x-31=2\left(\frac{0.03}{0.03}+\frac{0.02x}{0.03}\right)$$

Divide 0.03 by 0.03 to get 1.

$$0.6x-31=2\left(1+\frac{0.02x}{0.03}\right)$$

Divide 0.02x by 0.03 to get \frac{2}{3}x.

$$0.6x-31=2\left(1+\frac{2}{3}x\right)$$

Use the distributive property to multiply 2 by 1+\frac{2}{3}x.

$$0.6x-31=2+\frac{4}{3}x$$

Subtract \frac{4}{3}x from both sides.

$$0.6x-31-\frac{4}{3}x=2$$

Combine 0.6x and -\frac{4}{3}x to get -\frac{11}{15}x.

$$-\frac{11}{15}x-31=2$$

Add 31 to both sides.

$$-\frac{11}{15}x=2+31$$

Add 2 and 31 to get 33.

$$-\frac{11}{15}x=33$$

Divide both sides by -\frac{11}{15}.

$$x=\frac{33}{-\frac{11}{15}}$$