Q16. Simplify each expression聽1216-4... [FREE SOLUTION]

91影视

Chapter 1: Q16. (page 15)

Simplify each expression
$\frac{1}{2} (16 - 4 a) - \frac{3}{4} (12 + 20 a)$

Short Answer

Expert verified

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

Step by step solution

- Write properties of real numbers

Properties of real numbers are written in following table:

For any real numbers $a, b,$ and c:
Property	Addition	Multiplication
Commutative	$a + b = b + a$	$a 路 b = b 路 a$
Associative	$(a + b) + c = a + (b + c)$	$(a 路 b) 路 c = a 路 (b 路 c)$
Identity	$a + 0 = a = 0 + a$	$a 路 1 = a = 1 路 a$
Inverse	$a + (- a) = 0 = (- a) + a$	If $a 鈮� 0$ , then $a 路 \frac{1}{a} = 1 = \frac{1}{a} 路 a$
Distributive	$a (b + c) = a b + a c and (b + c) a = b a + c a$

- Simplify by grouping same variables

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

$\begin{matrix} \frac{1}{2} (16 鈭� 4 a) 鈭� \frac{3}{4} (12 + 20 a) = (\frac{1}{2} 鈰� 16) 鈭� (\frac{1}{2} 鈰� 4 a) 鈭� (\frac{3}{4} 鈰� 12) 鈭� (\frac{3}{4} 鈰� 20 a) \\ = 8 鈭� 2 a 鈭� 9 鈭� 15 a \\ = 8 鈭� 9 鈭� 2 a 鈭� 15 a \\ = (8 鈭� 9) 鈭� (2 + 15) a \end{matrix}$

- Simplify parentheses

Simplify parentheses by adding or subtracting the terms as shown below

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify each expression
$\frac{1}{2} (16 - 4 a) - \frac{3}{4} (12 + 20 a)$

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Simplify parentheses

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Discrete Mathematics

Probability and Statistics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

91影视

Simplify each expression1216-4a-3412+20a

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Simplify parentheses

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Discrete Mathematics

Probability and Statistics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Simplify each expression
$\frac{1}{2} (16 - 4 a) - \frac{3}{4} (12 + 20 a)$