Solve -4(x-5)=1/2(x+1)

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

Solve for x

$$x = \frac{13}{3} = 4\frac{1}{3} \approx 4.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply -4 by x-5.

$$-4x+20=\frac{1}{2}\left(x+1\right)$$

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

$$-4x+20=\frac{1}{2}x+\frac{1}{2}$$

Subtract \frac{1}{2}x from both sides.

$$-4x+20-\frac{1}{2}x=\frac{1}{2}$$

Combine -4x and -\frac{1}{2}x to get -\frac{9}{2}x.

$$-\frac{9}{2}x+20=\frac{1}{2}$$

Subtract 20 from both sides.

$$-\frac{9}{2}x=\frac{1}{2}-20$$

Convert 20 to fraction \frac{40}{2}.

$$-\frac{9}{2}x=\frac{1}{2}-\frac{40}{2}$$

Since \frac{1}{2} and \frac{40}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{9}{2}x=\frac{1-40}{2}$$

Subtract 40 from 1 to get -39.

$$-\frac{9}{2}x=-\frac{39}{2}$$

Multiply both sides by -\frac{2}{9}, the reciprocal of -\frac{9}{2}.

$$x=-\frac{39}{2}\left(-\frac{2}{9}\right)$$

Multiply -\frac{39}{2} times -\frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-39\left(-2\right)}{2\times 9}$$

Do the multiplications in the fraction \frac{-39\left(-2\right)}{2\times 9}.

$$x=\frac{78}{18}$$

Reduce the fraction \frac{78}{18} to lowest terms by extracting and canceling out 6.

$$x=\frac{13}{3}$$