Solve 2.4x-7/0.5-x-5/2=0.03+0.02x/0.03

$$\frac { 2.4 x - 7 } { 0.5 } - \frac { x - 5 } { 2 } = \frac { 0.03 + 0.02 x } { 0.03 }$$

Solve for x

$$x = \frac{375}{109} = 3\frac{48}{109} \approx 3.440366972$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\times \frac{2.4x-7}{0.5}-\left(x-5\right)=2\times \frac{0.03+0.02x}{0.03}$$

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

$$2\times \frac{2.4x-7}{0.5}-x-\left(-5\right)=2\times \frac{0.03+0.02x}{0.03}$$

The opposite of -5 is 5.

$$2\times \frac{2.4x-7}{0.5}-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Divide each term of 2.4x-7 by 0.5 to get \frac{2.4x}{0.5}+\frac{-7}{0.5}.

$$2\left(\frac{2.4x}{0.5}+\frac{-7}{0.5}\right)-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Divide 2.4x by 0.5 to get 4.8x.

$$2\left(4.8x+\frac{-7}{0.5}\right)-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Expand \frac{-7}{0.5} by multiplying both numerator and the denominator by 10.

$$2\left(4.8x+\frac{-70}{5}\right)-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Divide -70 by 5 to get -14.

$$2\left(4.8x-14\right)-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Use the distributive property to multiply 2 by 4.8x-14.

$$9.6x-28-x+5=2\times \frac{0.03+0.02x}{0.03}$$

Combine 9.6x and -x to get 8.6x.

$$8.6x-28+5=2\times \frac{0.03+0.02x}{0.03}$$

Add -28 and 5 to get -23.

$$8.6x-23=2\times \frac{0.03+0.02x}{0.03}$$

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

$$8.6x-23=2\left(\frac{0.03}{0.03}+\frac{0.02x}{0.03}\right)$$

Divide 0.03 by 0.03 to get 1.

$$8.6x-23=2\left(1+\frac{0.02x}{0.03}\right)$$

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

$$8.6x-23=2\left(1+\frac{2}{3}x\right)$$

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

$$8.6x-23=2+\frac{4}{3}x$$

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

$$8.6x-23-\frac{4}{3}x=2$$

Combine 8.6x and -\frac{4}{3}x to get \frac{109}{15}x.

$$\frac{109}{15}x-23=2$$

Add 23 to both sides.

$$\frac{109}{15}x=2+23$$

Add 2 and 23 to get 25.

$$\frac{109}{15}x=25$$

Divide both sides by \frac{109}{15}.

$$x=\frac{25}{\frac{109}{15}}$$