Solve 4x-15/05-5x-0,3/0,2=12x/0,1+3

$$\frac { 4 x - 15 } { 05 } - \frac { 5 x - 0,3 } { 0,2 } = \frac { 12 x } { 0,1 } + 3$$

Solve for x

$$x=-\frac{45}{1442}\approx -0,031206657$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$4x-15-5\times \frac{5x-0,3}{0,2}=5\times \frac{12x}{0,1}+15$$

Divide 12x by 0,1 to get 120x.

$$4x-15-5\times \frac{5x-0,3}{0,2}=5\times 120x+15$$

Multiply 5 and 120 to get 600.

$$4x-15-5\times \frac{5x-0,3}{0,2}=600x+15$$

Divide each term of 5x-0,3 by 0,2 to get \frac{5x}{0,2}+\frac{-0,3}{0,2}.

$$4x-15-5\left(\frac{5x}{0,2}+\frac{-0,3}{0,2}\right)=600x+15$$

Divide 5x by 0,2 to get 25x.

$$4x-15-5\left(25x+\frac{-0,3}{0,2}\right)=600x+15$$

Expand \frac{-0,3}{0,2} by multiplying both numerator and the denominator by 10.

$$4x-15-5\left(25x+\frac{-3}{2}\right)=600x+15$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$4x-15-5\left(25x-\frac{3}{2}\right)=600x+15$$

Use the distributive property to multiply -5 by 25x-\frac{3}{2}.

$$4x-15-125x-5\left(-\frac{3}{2}\right)=600x+15$$

Express -5\left(-\frac{3}{2}\right) as a single fraction.

$$4x-15-125x+\frac{-5\left(-3\right)}{2}=600x+15$$

Multiply -5 and -3 to get 15.

$$4x-15-125x+\frac{15}{2}=600x+15$$

Combine 4x and -125x to get -121x.

$$-121x-15+\frac{15}{2}=600x+15$$

Convert -15 to fraction -\frac{30}{2}.

$$-121x-\frac{30}{2}+\frac{15}{2}=600x+15$$

Since -\frac{30}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$-121x+\frac{-30+15}{2}=600x+15$$

Add -30 and 15 to get -15.

$$-121x-\frac{15}{2}=600x+15$$

Subtract 600x from both sides.

$$-121x-\frac{15}{2}-600x=15$$

Combine -121x and -600x to get -721x.

$$-721x-\frac{15}{2}=15$$

Add \frac{15}{2} to both sides.

$$-721x=15+\frac{15}{2}$$

Convert 15 to fraction \frac{30}{2}.

$$-721x=\frac{30}{2}+\frac{15}{2}$$

Since \frac{30}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$-721x=\frac{30+15}{2}$$

Add 30 and 15 to get 45.

$$-721x=\frac{45}{2}$$

Divide both sides by -721.

$$x=\frac{\frac{45}{2}}{-721}$$

Express \frac{\frac{45}{2}}{-721} as a single fraction.

$$x=\frac{45}{2\left(-721\right)}$$

Multiply 2 and -721 to get -1442.

$$x=\frac{45}{-1442}$$

Fraction \frac{45}{-1442} can be rewritten as -\frac{45}{1442} by extracting the negative sign.

$$x=-\frac{45}{1442}$$