Chapter 1: Q58. (page 16)

Simplify each expression
$\frac{1}{6} (3 x + 5 y) + \frac{2}{3} (\frac{3}{5} x - 6 y)$

Short Answer

Expert verified

$\frac{1}{6} (3 x + 5 y) + \frac{2}{3} (\frac{3}{5} x - 6 y)$ is simplified to $\frac{9}{10} x - \frac{19}{6} y$

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	$a \cdot b = b \cdot a$
Associative	$(a + b) + c = a + (b + c)$	$(a \cdot b) \cdot c = a \cdot (b \cdot c)$
Identity	a+0=a=0+a	$a \cdot 1 = a = 1 \cdot a$
Inverse	$a + (- a) = 0 = (- a) + a$	If $a \neq 0$ , then $a \cdot \frac{1}{a} = 1 = \frac{1}{a} \cdot a$
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

$\begin{matrix} \frac{1}{6} (3 x + 5 y) + \frac{2}{3} (\frac{3}{5} x - 6 y) = \frac{3}{6} x + \frac{5}{6} y + \frac{2}{5} x - 4 y \\ = \frac{3}{6} x + \frac{2}{5} x + \frac{5}{6} y - 4 y \\ = (\frac{3}{6} + \frac{2}{5}) x + (\frac{5}{6} - 4) y \end{matrix}$

- Simplify further

To simplify, evaluate parentheses as shown below

$\begin{matrix} (\frac{3}{6} + \frac{2}{5}) x + (\frac{5}{6} - 4) y = (\frac{(3 \cdot 5) + (2 \cdot 6)}{30}) x + (\frac{5 - (4 \cdot 6)}{6}) y \\ = (\frac{15 + 12}{30}) x + (\frac{5 - 24}{6}) y \\ = (\frac{27}{30}) x + (\frac{- 19}{6}) y \\ = \frac{9}{10} x - \frac{19}{6} y \end{matrix}$

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Simplify each expression
$\frac{1}{6} (3 x + 5 y) + \frac{2}{3} (\frac{3}{5} x - 6 y)$

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Simplify further

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Simplify each expression163x+5y+2335x-6y

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

Mechanics Maths

Probability and Statistics

Decision Maths

Pure Maths

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Simplify each expression
$\frac{1}{6} (3 x + 5 y) + \frac{2}{3} (\frac{3}{5} x - 6 y)$