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Q16.

Expert-verifiedFound in: Page 15

Book edition
Middle English Edition

Author(s)
Carter

Pages
804 pages

ISBN
9780079039903

**Simplify each expression**

** $\frac{1}{2}\left(16-4a\right)-\frac{3}{4}\left(12+20a\right)$**

$\frac{1}{2}\left(16-4a\right)-\frac{3}{4}\left(12+20a\right)$ is simplified to $-1-17a$

Properties of real numbers are written in following table:

For any real numbers $a,b,$ and c: | ||

Property | Addition | Multiplication |

Commutative | $a+b=b+a$ | $a\xb7b=b\xb7a$ |

Associative | $\left(a+b\right)+c=a+\left(b+c\right)$ | $\left(a\xb7b\right)\xb7c=a\xb7\left(b\xb7c\right)$ |

Identity | $a+0=a=0+a$ | $a\xb71=a=1\xb7a$ |

Inverse | $a+\left(-a\right)=0=\left(-a\right)+a$ | If $a\ne 0$, then $a\xb7\frac{1}{a}=1=\frac{1}{a}\xb7a$ |

Distributive | $a\left(b+c\right)=ab+ac\text{and}\left(b+c\right)a=ba+ca$ |

To simplify given equation, use commutative and distributive property to group coefficients of same variable as shown below

$\begin{array}{c}\frac{1}{2}\left(16-4a\right)-\frac{3}{4}\left(12+20a\right)=\left(\frac{1}{2}\cdot 16\right)-\left(\frac{1}{2}\cdot 4a\right)-\left(\frac{3}{4}\cdot 12\right)-\left(\frac{3}{4}\cdot 20a\right)\\ =8-2a-9-15a\\ =8-9-2a-15a\\ =\left(8-9\right)-\left(2+15\right)a\end{array}$

Simplify parentheses by adding or subtracting the terms as shown below

$\left(8-9\right)-\left(2+15\right)a=-1-17a$

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