Solve 1/2[(3a+2b)-(a+1/2b)]-2(1/2a+3/8b)

$$\frac { 1 } { 2 } [ ( 3 a + 2 b ) - ( a + \frac { 1 } { 2 } b ) ] - 2 ( \frac { 1 } { 2 } a + \frac { 3 } { 8 } b )$$

Evaluate

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Solution Steps

To find the opposite of a+\frac{1}{2}b, find the opposite of each term.

$$\frac{1}{2}\left(3a+2b-a-\frac{1}{2}b\right)-2\left(\frac{1}{2}a+\frac{3}{8}b\right)$$

Combine 3a and -a to get 2a.

$$\frac{1}{2}\left(2a+2b-\frac{1}{2}b\right)-2\left(\frac{1}{2}a+\frac{3}{8}b\right)$$

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

$$\frac{1}{2}\left(2a+\frac{3}{2}b\right)-2\left(\frac{1}{2}a+\frac{3}{8}b\right)$$

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

$$\frac{1}{2}\times 2a+\frac{1}{2}\times \frac{3}{2}b-2\left(\frac{1}{2}a+\frac{3}{8}b\right)$$

Cancel out 2 and 2.

$$a+\frac{1}{2}\times \frac{3}{2}b-2\left(\frac{1}{2}a+\frac{3}{8}b\right)$$

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

$$a+\frac{1\times 3}{2\times 2}b-2\left(\frac{1}{2}a+\frac{3}{8}b\right)$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 2}.

$$a+\frac{3}{4}b-2\left(\frac{1}{2}a+\frac{3}{8}b\right)$$

Use the distributive property to multiply -2 by \frac{1}{2}a+\frac{3}{8}b.

$$a+\frac{3}{4}b-2\times \frac{1}{2}a-2\times \frac{3}{8}b$$

Multiply -2 times \frac{1}{2}.

$$a+\frac{3}{4}b-a-2\times \frac{3}{8}b$$

Express -2\times \frac{3}{8} as a single fraction.

$$a+\frac{3}{4}b-a+\frac{-2\times 3}{8}b$$

Multiply -2 and 3 to get -6.

$$a+\frac{3}{4}b-a+\frac{-6}{8}b$$

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

$$a+\frac{3}{4}b-a-\frac{3}{4}b$$

Combine a and -a to get 0.

$$\frac{3}{4}b-\frac{3}{4}b$$

Combine \frac{3}{4}b and -\frac{3}{4}b to get 0.

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Factor

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Solution Steps

Factor out \frac{1}{4}.

$$\frac{6a+4b-\left(2a+b\right)-\left(4a+3b\right)}{4}$$

Simplify.

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