Solve 0.5x+2/0.03-x=0.3(0.5x+2)/0.2-1011/12

$$\frac { 0.5 x + 2 } { 0.03 } - x = \frac { 0.3 ( 0.5 x + 2 ) } { 0.2 } - 10 \frac { 11 } { 12 }$$

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12.

$$12\times \frac{0.5x+2}{0.03}-12x=12\times \frac{0.3\left(0.5x+2\right)}{0.2}-\left(10\times 12+11\right)$$

Use the distributive property to multiply 0.3 by 0.5x+2.

$$12\times \frac{0.5x+2}{0.03}-12x=12\times \frac{0.15x+0.6}{0.2}-\left(10\times 12+11\right)$$

Multiply 10 and 12 to get 120.

$$12\times \frac{0.5x+2}{0.03}-12x=12\times \frac{0.15x+0.6}{0.2}-\left(120+11\right)$$

Add 120 and 11 to get 131.

$$12\times \frac{0.5x+2}{0.03}-12x=12\times \frac{0.15x+0.6}{0.2}-131$$

Divide each term of 0.5x+2 by 0.03 to get \frac{0.5x}{0.03}+\frac{2}{0.03}.

$$12\left(\frac{0.5x}{0.03}+\frac{2}{0.03}\right)-12x=12\times \frac{0.15x+0.6}{0.2}-131$$

Divide 0.5x by 0.03 to get \frac{50}{3}x.

$$12\left(\frac{50}{3}x+\frac{2}{0.03}\right)-12x=12\times \frac{0.15x+0.6}{0.2}-131$$

Expand \frac{2}{0.03} by multiplying both numerator and the denominator by 100.

$$12\left(\frac{50}{3}x+\frac{200}{3}\right)-12x=12\times \frac{0.15x+0.6}{0.2}-131$$

Use the distributive property to multiply 12 by \frac{50}{3}x+\frac{200}{3}.

$$200x+12\times \frac{200}{3}-12x=12\times \frac{0.15x+0.6}{0.2}-131$$

Express 12\times \frac{200}{3} as a single fraction.

$$200x+\frac{12\times 200}{3}-12x=12\times \frac{0.15x+0.6}{0.2}-131$$

Multiply 12 and 200 to get 2400.

$$200x+\frac{2400}{3}-12x=12\times \frac{0.15x+0.6}{0.2}-131$$

Divide 2400 by 3 to get 800.

$$200x+800-12x=12\times \frac{0.15x+0.6}{0.2}-131$$

Combine 200x and -12x to get 188x.

$$188x+800=12\times \frac{0.15x+0.6}{0.2}-131$$

Divide each term of 0.15x+0.6 by 0.2 to get \frac{0.15x}{0.2}+\frac{0.6}{0.2}.

$$188x+800=12\left(\frac{0.15x}{0.2}+\frac{0.6}{0.2}\right)-131$$

Divide 0.15x by 0.2 to get 0.75x.

$$188x+800=12\left(0.75x+\frac{0.6}{0.2}\right)-131$$

Expand \frac{0.6}{0.2} by multiplying both numerator and the denominator by 10.

$$188x+800=12\left(0.75x+\frac{6}{2}\right)-131$$

Divide 6 by 2 to get 3.

$$188x+800=12\left(0.75x+3\right)-131$$

Use the distributive property to multiply 12 by 0.75x+3.

$$188x+800=9x+36-131$$

Subtract 131 from 36 to get -95.

$$188x+800=9x-95$$

Subtract 9x from both sides.

$$188x+800-9x=-95$$

Combine 188x and -9x to get 179x.

$$179x+800=-95$$

Subtract 800 from both sides.

$$179x=-95-800$$

Subtract 800 from -95 to get -895.

$$179x=-895$$

Divide both sides by 179.

$$x=\frac{-895}{179}$$

Divide -895 by 179 to get -5.

$$x=-5$$