Solve 0.3x+0.2/0.4-5x+1/2=2-0.07x-0.01/0.03

$$\frac { 0.3 x + 0.2 } { 0.4 } - \frac { 5 x + 1 } { 2 } = 2 - \frac { 0.07 x - 0.01 } { 0.03 }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\times \frac{0.3x+0.2}{0.4}-\left(5x+1\right)=4-2\times \frac{0.07x-0.01}{0.03}$$

To find the opposite of 5x+1, find the opposite of each term.

$$2\times \frac{0.3x+0.2}{0.4}-5x-1=4-2\times \frac{0.07x-0.01}{0.03}$$

Divide each term of 0.3x+0.2 by 0.4 to get \frac{0.3x}{0.4}+\frac{0.2}{0.4}.

$$2\left(\frac{0.3x}{0.4}+\frac{0.2}{0.4}\right)-5x-1=4-2\times \frac{0.07x-0.01}{0.03}$$

Divide 0.3x by 0.4 to get 0.75x.

$$2\left(0.75x+\frac{0.2}{0.4}\right)-5x-1=4-2\times \frac{0.07x-0.01}{0.03}$$

Expand \frac{0.2}{0.4} by multiplying both numerator and the denominator by 10.

$$2\left(0.75x+\frac{2}{4}\right)-5x-1=4-2\times \frac{0.07x-0.01}{0.03}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$2\left(0.75x+\frac{1}{2}\right)-5x-1=4-2\times \frac{0.07x-0.01}{0.03}$$

Use the distributive property to multiply 2 by 0.75x+\frac{1}{2}.

$$1.5x+2\times \frac{1}{2}-5x-1=4-2\times \frac{0.07x-0.01}{0.03}$$

Cancel out 2 and 2.

$$1.5x+1-5x-1=4-2\times \frac{0.07x-0.01}{0.03}$$

Combine 1.5x and -5x to get -3.5x.

$$-3.5x+1-1=4-2\times \frac{0.07x-0.01}{0.03}$$

Subtract 1 from 1 to get 0.

$$-3.5x=4-2\times \frac{0.07x-0.01}{0.03}$$

Divide each term of 0.07x-0.01 by 0.03 to get \frac{0.07x}{0.03}+\frac{-0.01}{0.03}.

$$-3.5x=4-2\left(\frac{0.07x}{0.03}+\frac{-0.01}{0.03}\right)$$

Divide 0.07x by 0.03 to get \frac{7}{3}x.

$$-3.5x=4-2\left(\frac{7}{3}x+\frac{-0.01}{0.03}\right)$$

Expand \frac{-0.01}{0.03} by multiplying both numerator and the denominator by 100.

$$-3.5x=4-2\left(\frac{7}{3}x+\frac{-1}{3}\right)$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$-3.5x=4-2\left(\frac{7}{3}x-\frac{1}{3}\right)$$

Use the distributive property to multiply -2 by \frac{7}{3}x-\frac{1}{3}.

$$-3.5x=4-\frac{14}{3}x-2\left(-\frac{1}{3}\right)$$

Express -2\left(-\frac{1}{3}\right) as a single fraction.

$$-3.5x=4-\frac{14}{3}x+\frac{-2\left(-1\right)}{3}$$

Multiply -2 and -1 to get 2.

$$-3.5x=4-\frac{14}{3}x+\frac{2}{3}$$

Convert 4 to fraction \frac{12}{3}.

$$-3.5x=\frac{12}{3}-\frac{14}{3}x+\frac{2}{3}$$

Since \frac{12}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$-3.5x=\frac{12+2}{3}-\frac{14}{3}x$$

Add 12 and 2 to get 14.

$$-3.5x=\frac{14}{3}-\frac{14}{3}x$$

Add \frac{14}{3}x to both sides.

$$-3.5x+\frac{14}{3}x=\frac{14}{3}$$

Combine -3.5x and \frac{14}{3}x to get \frac{7}{6}x.

$$\frac{7}{6}x=\frac{14}{3}$$

Divide both sides by \frac{7}{6}.

$$x=\frac{\frac{14}{3}}{\frac{7}{6}}$$

Express \frac{\frac{14}{3}}{\frac{7}{6}} as a single fraction.

$$x=\frac{14}{3\times \frac{7}{6}}$$

Multiply 3 and \frac{7}{6} to get 3.5.

$$x=\frac{14}{3.5}$$

Expand \frac{14}{3.5} by multiplying both numerator and the denominator by 10.

$$x=\frac{140}{35}$$

Divide 140 by 35 to get 4.

$$x=4$$