Q57. Simplify each expression146+20y-... [FREE SOLUTION]

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Chapter 1: Q57. (page 16)

Simplify each expression
$\frac{1}{4} (6 + 20 y) - \frac{1}{2} (19 - 8 y)$

Short Answer

Expert verified

$\frac{1}{4} (6 + 20 y) - \frac{1}{2} (19 - 8 y)$ is simplified to $- 8 + 9 y$

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, first use distributive property then commutative property of addition then distributive property to group coefficients of same variable as shown below

$\begin{matrix} \frac{1}{4} (6 + 20 y) 鈭� \frac{1}{2} (19 鈭� 8 y) = \frac{6}{4} + \frac{20}{4} y 鈭� \frac{19}{2} + \frac{8}{2} y \\ = \frac{3}{2} + 5 y 鈭� \frac{19}{2} + 4 y \\ = \frac{3}{2} 鈭� \frac{19}{2} + 5 y + 4 y \\ = \frac{1}{2} (3 鈭� 19) + (5 + 4) y \end{matrix}$

- Simplify further

To simplify, evaluate parentheses as shown below

$\begin{matrix} \frac{1}{2} (3 鈭� 19) + (5 + 4) y = \frac{1}{2} (鈭� 16) + 9 y \\ = 鈭� 8 + 9 y \end{matrix}$

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91影视

Simplify each expression
$\frac{1}{4} (6 + 20 y) - \frac{1}{2} (19 - 8 y)$

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Simplify further

One App. One Place for Learning.

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91影视

Simplify each expression146+20y-1219-8y

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Simplify further

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Simplify each expression
$\frac{1}{4} (6 + 20 y) - \frac{1}{2} (19 - 8 y)$