Solve -3/8(-6-2y)=.5(2y-3)-1

$$- \frac{ 3 }{ 8 } (-6-2y)=.5(2y-3)-1$$

Solve for y

$$y=19$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{3}{8} by -6-2y.

$$-\frac{3}{8}\left(-6\right)-\frac{3}{8}\left(-2\right)y=0.5\left(2y-3\right)-1$$

Express -\frac{3}{8}\left(-6\right) as a single fraction.

$$\frac{-3\left(-6\right)}{8}-\frac{3}{8}\left(-2\right)y=0.5\left(2y-3\right)-1$$

Multiply -3 and -6 to get 18.

$$\frac{18}{8}-\frac{3}{8}\left(-2\right)y=0.5\left(2y-3\right)-1$$

Reduce the fraction \frac{18}{8} to lowest terms by extracting and canceling out 2.

$$\frac{9}{4}-\frac{3}{8}\left(-2\right)y=0.5\left(2y-3\right)-1$$

Express -\frac{3}{8}\left(-2\right) as a single fraction.

$$\frac{9}{4}+\frac{-3\left(-2\right)}{8}y=0.5\left(2y-3\right)-1$$

Multiply -3 and -2 to get 6.

$$\frac{9}{4}+\frac{6}{8}y=0.5\left(2y-3\right)-1$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{9}{4}+\frac{3}{4}y=0.5\left(2y-3\right)-1$$

Use the distributive property to multiply 0.5 by 2y-3.

$$\frac{9}{4}+\frac{3}{4}y=y-1.5-1$$

Subtract 1 from -1.5 to get -2.5.

$$\frac{9}{4}+\frac{3}{4}y=y-2.5$$

Subtract y from both sides.

$$\frac{9}{4}+\frac{3}{4}y-y=-2.5$$

Combine \frac{3}{4}y and -y to get -\frac{1}{4}y.

$$\frac{9}{4}-\frac{1}{4}y=-2.5$$

Subtract \frac{9}{4} from both sides.

$$-\frac{1}{4}y=-2.5-\frac{9}{4}$$

Convert decimal number -2.5 to fraction -\frac{25}{10}. Reduce the fraction -\frac{25}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{4}y=-\frac{5}{2}-\frac{9}{4}$$

Least common multiple of 2 and 4 is 4. Convert -\frac{5}{2} and \frac{9}{4} to fractions with denominator 4.

$$-\frac{1}{4}y=-\frac{10}{4}-\frac{9}{4}$$

Since -\frac{10}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{4}y=\frac{-10-9}{4}$$

Subtract 9 from -10 to get -19.

$$-\frac{1}{4}y=-\frac{19}{4}$$

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

$$y=-\frac{19}{4}\left(-4\right)$$

Express -\frac{19}{4}\left(-4\right) as a single fraction.

$$y=\frac{-19\left(-4\right)}{4}$$

Multiply -19 and -4 to get 76.

$$y=\frac{76}{4}$$

Divide 76 by 4 to get 19.

$$y=19$$