Q13. Simplify each expression3x+4y-5x... [FREE SOLUTION]

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Chapter 1: Q13. (page 15)

Simplify each expression
$3 x + 4 y - 5 x$

Short Answer

Expert verified

$3 x + 4 y - 5 x$ is simplified to $- 2 (x - 2 y)$

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

$\begin{matrix} 3 x + 4 y 鈭� 5 x = 3 x 鈭� 5 x + 4 y \\ = (3 鈭� 5) x + 4 y \end{matrix}$

- Use distributive property

Firstly simplify parentheses then take out common factor of both terms as shown below

$\begin{matrix} (3 鈭� 5) x + 4 y = 鈭� 2 x + 4 y \\ = 鈭� 2 (x 鈭� 2 y) \end{matrix}$

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91影视

Simplify each expression
$3 x + 4 y - 5 x$

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Use distributive property

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