Solve 1/4(2x-1)=35/4-x

$$\frac { 1 } { 4 } ( 2 x - 1 ) = \frac { 35 } { 4 } - x$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by 2x-1.

$$\frac{1}{4}\times 2x+\frac{1}{4}\left(-1\right)=\frac{35}{4}-x$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{2}{4}x+\frac{1}{4}\left(-1\right)=\frac{35}{4}-x$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}x+\frac{1}{4}\left(-1\right)=\frac{35}{4}-x$$

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

$$\frac{1}{2}x-\frac{1}{4}=\frac{35}{4}-x$$

Add x to both sides.

$$\frac{1}{2}x-\frac{1}{4}+x=\frac{35}{4}$$

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

$$\frac{3}{2}x-\frac{1}{4}=\frac{35}{4}$$

Add \frac{1}{4} to both sides.

$$\frac{3}{2}x=\frac{35}{4}+\frac{1}{4}$$

Since \frac{35}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{3}{2}x=\frac{35+1}{4}$$

Add 35 and 1 to get 36.

$$\frac{3}{2}x=\frac{36}{4}$$

Divide 36 by 4 to get 9.

$$\frac{3}{2}x=9$$

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.

$$x=9\times \frac{2}{3}$$

Express 9\times \frac{2}{3} as a single fraction.

$$x=\frac{9\times 2}{3}$$

Multiply 9 and 2 to get 18.

$$x=\frac{18}{3}$$

Divide 18 by 3 to get 6.

$$x=6$$