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

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

Solve for x

$$x=-\frac{3}{8}=-0.375$$

Steps for Solving Linear Equation

Subtract \frac{3}{2}x from both sides.

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

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

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

Subtract \frac{3}{4} from both sides.

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

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{3}{4} to fractions with denominator 4.

$$-2x=\frac{6}{4}-\frac{3}{4}$$

Since \frac{6}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$-2x=\frac{6-3}{4}$$

Subtract 3 from 6 to get 3.

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

Divide both sides by -2.

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

Express \frac{\frac{3}{4}}{-2} as a single fraction.

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

Multiply 4 and -2 to get -8.

$$x=\frac{3}{-8}$$

Fraction \frac{3}{-8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$x=-\frac{3}{8}$$