Solve 2/5(x+1/2)=-3/4

$$\frac { 2 } { 5 } ( x + \frac { 1 } { 2 } ) = \frac { - 3 } { 4 }$$

Solve for x

$$x = -\frac{19}{8} = -2\frac{3}{8} = -2.375$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{5} by x+\frac{1}{2}.

$$\frac{2}{5}x+\frac{2}{5}\times \frac{1}{2}=\frac{-3}{4}$$

Multiply \frac{2}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}x+\frac{2\times 1}{5\times 2}=\frac{-3}{4}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2}{5}x+\frac{1}{5}=\frac{-3}{4}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{2}{5}x+\frac{1}{5}=-\frac{3}{4}$$

Subtract \frac{1}{5} from both sides.

$$\frac{2}{5}x=-\frac{3}{4}-\frac{1}{5}$$

Least common multiple of 4 and 5 is 20. Convert -\frac{3}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{2}{5}x=-\frac{15}{20}-\frac{4}{20}$$

Since -\frac{15}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}x=\frac{-15-4}{20}$$

Subtract 4 from -15 to get -19.

$$\frac{2}{5}x=-\frac{19}{20}$$

Multiply both sides by \frac{5}{2}, the reciprocal of \frac{2}{5}.

$$x=-\frac{19}{20}\times \frac{5}{2}$$

Multiply -\frac{19}{20} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-19\times 5}{20\times 2}$$

Do the multiplications in the fraction \frac{-19\times 5}{20\times 2}.

$$x=\frac{-95}{40}$$

Reduce the fraction \frac{-95}{40} to lowest terms by extracting and canceling out 5.

$$x=-\frac{19}{8}$$