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

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

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

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

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

Cancel out 4 and 4.

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

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

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

Subtract x from both sides.

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

Combine \frac{5}{4}x and -x to get \frac{1}{4}x.

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

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

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

Least common multiple of 4 and 2 is 4. Convert -\frac{1}{4} and \frac{1}{2} to fractions with denominator 4.

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

Since -\frac{1}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from -1 to get -3.

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

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

$$x=-\frac{3}{4}\times 4$$

Cancel out 4 and 4.

$$x=-3$$