Solve x=21+4(-5/8x-35/8)

$$x = 21 + 4 ( - \frac { 5 } { 8 } x - \frac { 35 } { 8 } )$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by -\frac{5}{8}x-\frac{35}{8}.

$$x=21+4\left(-\frac{5}{8}\right)x+4\left(-\frac{35}{8}\right)$$

Express 4\left(-\frac{5}{8}\right) as a single fraction.

$$x=21+\frac{4\left(-5\right)}{8}x+4\left(-\frac{35}{8}\right)$$

Multiply 4 and -5 to get -20.

$$x=21+\frac{-20}{8}x+4\left(-\frac{35}{8}\right)$$

Reduce the fraction \frac{-20}{8} to lowest terms by extracting and canceling out 4.

$$x=21-\frac{5}{2}x+4\left(-\frac{35}{8}\right)$$

Express 4\left(-\frac{35}{8}\right) as a single fraction.

$$x=21-\frac{5}{2}x+\frac{4\left(-35\right)}{8}$$

Multiply 4 and -35 to get -140.

$$x=21-\frac{5}{2}x+\frac{-140}{8}$$

Reduce the fraction \frac{-140}{8} to lowest terms by extracting and canceling out 4.

$$x=21-\frac{5}{2}x-\frac{35}{2}$$

Convert 21 to fraction \frac{42}{2}.

$$x=\frac{42}{2}-\frac{5}{2}x-\frac{35}{2}$$

Since \frac{42}{2} and \frac{35}{2} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{42-35}{2}-\frac{5}{2}x$$

Subtract 35 from 42 to get 7.

$$x=\frac{7}{2}-\frac{5}{2}x$$

Add \frac{5}{2}x to both sides.

$$x+\frac{5}{2}x=\frac{7}{2}$$

Combine x and \frac{5}{2}x to get \frac{7}{2}x.

$$\frac{7}{2}x=\frac{7}{2}$$

Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}.

$$x=\frac{7}{2}\times \frac{2}{7}$$

Cancel out \frac{7}{2} and its reciprocal \frac{2}{7}.

$$x=1$$