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

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

Solve for x

$$x = -\frac{162}{115} = -1\frac{47}{115} \approx -1.408695652$$

Steps for Solving Linear Equation

Divide 1 by \frac{1}{4} by multiplying 1 by the reciprocal of \frac{1}{4}.

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

Multiply 1 and 4 to get 4.

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

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

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

Subtract 6 from 2 to get -4.

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

Use the distributive property to multiply 4 by -4-3x.

$$-16-12x=\frac{1}{5}\left(-3x+1+\frac{1}{2}x\right)$$

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

$$-16-12x=\frac{1}{5}\left(-\frac{5}{2}x+1\right)$$

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

$$-16-12x=\frac{1}{5}\left(-\frac{5}{2}\right)x+\frac{1}{5}$$

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

$$-16-12x=\frac{1\left(-5\right)}{5\times 2}x+\frac{1}{5}$$

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

$$-16-12x=\frac{-5}{10}x+\frac{1}{5}$$

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

$$-16-12x=-\frac{1}{2}x+\frac{1}{5}$$

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

$$-16-12x+\frac{1}{2}x=\frac{1}{5}$$

Combine -12x and \frac{1}{2}x to get -\frac{23}{2}x.

$$-16-\frac{23}{2}x=\frac{1}{5}$$

Add 16 to both sides.

$$-\frac{23}{2}x=\frac{1}{5}+16$$

Convert 16 to fraction \frac{80}{5}.

$$-\frac{23}{2}x=\frac{1}{5}+\frac{80}{5}$$

Since \frac{1}{5} and \frac{80}{5} have the same denominator, add them by adding their numerators.

$$-\frac{23}{2}x=\frac{1+80}{5}$$

Add 1 and 80 to get 81.

$$-\frac{23}{2}x=\frac{81}{5}$$

Multiply both sides by -\frac{2}{23}, the reciprocal of -\frac{23}{2}.

$$x=\frac{81}{5}\left(-\frac{2}{23}\right)$$

Multiply \frac{81}{5} times -\frac{2}{23} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{81\left(-2\right)}{5\times 23}$$

Do the multiplications in the fraction \frac{81\left(-2\right)}{5\times 23}.

$$x=\frac{-162}{115}$$

Fraction \frac{-162}{115} can be rewritten as -\frac{162}{115} by extracting the negative sign.

$$x=-\frac{162}{115}$$