Solve 9/4a-3/2(2a-1)+1=3

$$\frac { 9 } { 4 } a - \frac { 3 } { 2 } ( 2 a - 1 ) + 1 = 3$$

Solve for a

$$a=-\frac{2}{3}\approx -0.666666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{3}{2} by 2a-1.

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

Cancel out 2 and 2.

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

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

$$\frac{9}{4}a-3a+\frac{3}{2}+1=3$$

Combine \frac{9}{4}a and -3a to get -\frac{3}{4}a.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{3}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

Add 3 and 2 to get 5.

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

Subtract \frac{5}{2} from both sides.

$$-\frac{3}{4}a=3-\frac{5}{2}$$

Convert 3 to fraction \frac{6}{2}.

$$-\frac{3}{4}a=\frac{6}{2}-\frac{5}{2}$$

Since \frac{6}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{4}a=\frac{6-5}{2}$$

Subtract 5 from 6 to get 1.

$$-\frac{3}{4}a=\frac{1}{2}$$

Multiply both sides by -\frac{4}{3}, the reciprocal of -\frac{3}{4}.

$$a=\frac{1}{2}\left(-\frac{4}{3}\right)$$

Multiply \frac{1}{2} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{1\left(-4\right)}{2\times 3}$$

Do the multiplications in the fraction \frac{1\left(-4\right)}{2\times 3}.

$$a=\frac{-4}{6}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$a=-\frac{2}{3}$$