Solve 2x-13/4/4+2x+3/2=-1

$$\frac { 2 x - \frac { 13 } { 4 } } { 4 } + \frac { 2 x + 3 } { 2 } = - 1$$

Solve for x

$$x = -\frac{9}{8} = -1\frac{1}{8} = -1.125$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$2x-\frac{13}{4}+2\left(2x+3\right)=-4$$

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

$$2x-\frac{13}{4}+4x+6=-4$$

Combine 2x and 4x to get 6x.

$$6x-\frac{13}{4}+6=-4$$

Convert 6 to fraction \frac{24}{4}.

$$6x-\frac{13}{4}+\frac{24}{4}=-4$$

Since -\frac{13}{4} and \frac{24}{4} have the same denominator, add them by adding their numerators.

$$6x+\frac{-13+24}{4}=-4$$

Add -13 and 24 to get 11.

$$6x+\frac{11}{4}=-4$$

Subtract \frac{11}{4} from both sides.

$$6x=-4-\frac{11}{4}$$

Convert -4 to fraction -\frac{16}{4}.

$$6x=-\frac{16}{4}-\frac{11}{4}$$

Since -\frac{16}{4} and \frac{11}{4} have the same denominator, subtract them by subtracting their numerators.

$$6x=\frac{-16-11}{4}$$

Subtract 11 from -16 to get -27.

$$6x=-\frac{27}{4}$$

Divide both sides by 6.

$$x=\frac{-\frac{27}{4}}{6}$$

Express \frac{-\frac{27}{4}}{6} as a single fraction.

$$x=\frac{-27}{4\times 6}$$

Multiply 4 and 6 to get 24.

$$x=\frac{-27}{24}$$

Reduce the fraction \frac{-27}{24} to lowest terms by extracting and canceling out 3.

$$x=-\frac{9}{8}$$