Solve 1/4[2-3(x+2)]=1/5[(-3x+1)+1/2x]}

$$\frac { 1 } { 4 } [ 2 - 3 ( x + 2 ) ] = \frac { 1 } { 5 } [ ( - 3 x + 1 ) + \frac { 1 } { 2 } x ] \}$$

Solve for x

$$x = -\frac{24}{5} = -4\frac{4}{5} = -4.8$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by x+2.

$$\frac{1}{4}\left(2-3x-6\right)=\frac{1}{5}\left(-3x+1+\frac{1}{2}x\right)$$

Subtract 6 from 2 to get -4.

$$\frac{1}{4}\left(-4-3x\right)=\frac{1}{5}\left(-3x+1+\frac{1}{2}x\right)$$

Use the distributive property to multiply \frac{1}{4} by -4-3x.

$$\frac{1}{4}\left(-4\right)+\frac{1}{4}\left(-3\right)x=\frac{1}{5}\left(-3x+1+\frac{1}{2}x\right)$$

Multiply \frac{1}{4} and -4 to get \frac{-4}{4}.

$$\frac{-4}{4}+\frac{1}{4}\left(-3\right)x=\frac{1}{5}\left(-3x+1+\frac{1}{2}x\right)$$

Divide -4 by 4 to get -1.

$$-1+\frac{1}{4}\left(-3\right)x=\frac{1}{5}\left(-3x+1+\frac{1}{2}x\right)$$

Multiply \frac{1}{4} and -3 to get \frac{-3}{4}.

$$-1+\frac{-3}{4}x=\frac{1}{5}\left(-3x+1+\frac{1}{2}x\right)$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$-1-\frac{3}{4}x=\frac{1}{5}\left(-3x+1+\frac{1}{2}x\right)$$

Combine -3x and \frac{1}{2}x to get -\frac{5}{2}x.

$$-1-\frac{3}{4}x=\frac{1}{5}\left(-\frac{5}{2}x+1\right)$$

Use the distributive property to multiply \frac{1}{5} by -\frac{5}{2}x+1.

$$-1-\frac{3}{4}x=\frac{1}{5}\left(-\frac{5}{2}\right)x+\frac{1}{5}$$

Multiply \frac{1}{5} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$-1-\frac{3}{4}x=\frac{1\left(-5\right)}{5\times 2}x+\frac{1}{5}$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{5\times 2}.

$$-1-\frac{3}{4}x=\frac{-5}{10}x+\frac{1}{5}$$

Reduce the fraction \frac{-5}{10} to lowest terms by extracting and canceling out 5.

$$-1-\frac{3}{4}x=-\frac{1}{2}x+\frac{1}{5}$$

Add \frac{1}{2}x to both sides.

$$-1-\frac{3}{4}x+\frac{1}{2}x=\frac{1}{5}$$

Combine -\frac{3}{4}x and \frac{1}{2}x to get -\frac{1}{4}x.

$$-1-\frac{1}{4}x=\frac{1}{5}$$

Add 1 to both sides.

$$-\frac{1}{4}x=\frac{1}{5}+1$$

Convert 1 to fraction \frac{5}{5}.

$$-\frac{1}{4}x=\frac{1}{5}+\frac{5}{5}$$

Since \frac{1}{5} and \frac{5}{5} have the same denominator, add them by adding their numerators.

$$-\frac{1}{4}x=\frac{1+5}{5}$$

Add 1 and 5 to get 6.

$$-\frac{1}{4}x=\frac{6}{5}$$

Multiply both sides by -4, the reciprocal of -\frac{1}{4}.

$$x=\frac{6}{5}\left(-4\right)$$

Express \frac{6}{5}\left(-4\right) as a single fraction.

$$x=\frac{6\left(-4\right)}{5}$$

Multiply 6 and -4 to get -24.

$$x=\frac{-24}{5}$$

Fraction \frac{-24}{5} can be rewritten as -\frac{24}{5} by extracting the negative sign.

$$x=-\frac{24}{5}$$