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Math0075 910 preview assignment 15 d

Math0075 910 preview assignment 15 d

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Foundations of Mathematical Reasoning Version 3.0 (2020)

Student Pages

Preview Assignment 15.D

Preparing for the next class

In the next class, you will need to know how to apply the order of operations when

simplifying an expression, how to square a number, and how to solve a two-step linear

equation.

Simplifying expressions

When solving equations, you may need to simplify algebraic expressions as much as

possible.

For example:

3(5𝑥 + 1) simplifies to 3 ∙ 5𝑥 + 3 ∙ 1 and

10𝑥 − 3𝑥 simplifies to 7𝑥

We say that 3(5𝑥 + 1) is equivalent to 3 ∙ 5𝑥 + 3 ∙ 1, and 10𝑥 − 3𝑥 is equivalent to 7𝑥.

1) Which expressions are equivalent to the expression below? There may be more

than one correct answer.

2(5𝑥 + 4) – 3𝑥 + 1

a) 10𝑥 + 8 – 3𝑥 + 1

b) 18𝑥 – 3𝑥 + 1

c) 15𝑥 + 1

d) 7𝑥 + 9

2) Which expressions are equivalent to the expression below? There may be more

than one correct answer.

−3(2𝑥 – 1) + 3(𝑥 + 1) − 4𝑥

a) −6𝑥 + 3 + 3𝑥 + 3 − 4𝑥

b) −10𝑥 + 6 + 3𝑥

c) −𝑥 + 12

d) 7𝑥 + 6

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Foundations of Mathematical Reasoning Version 3.0 (2020)

Student Pages

Exponents

It is important to pay careful attention to notation when working with negatives. For

example, – 5

is not the same as (–5)

. You can verify this by evaluating each

expression on a calculator. The order of operations is the reason for this difference. The

negative in each expression can be thought of as multiplication by – 1. Look at the

expressions rewritten with a – 1 and think about what operation you would perform first.

−1 ∙ 5

(−1 ∙ 5)

In the first expression, the exponent is done first: −1 ∙ 5

→ −1 ∙ 25 → −25.

In the second expression, the multiplication is done first: (−1 ∙ 5)

→ (– 5)

→ 25.

3) Simplify each of the following:

Part A: 5

= 25

Part B: −3

= -9

Part C: (−4)

= 16

Part D: −4

= -16

Part E: −(−6)

= -36

4) Simplify the following expression:

−5

− (−3)

+ 6

= 2

5) Solve 5 =

𝑥

− 3 32

6) Solve

𝑥 +7

= 6 5

7) Solve

𝑥 −14

= 2𝑥 -2

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Foundations of Mathematical Reasoning Version 3.0 (2020) Student Pages Preview Assignment 15.D Preparing for the next class In the next class, you will need to know how to apply the order of operations when simplifying an expression, how to square a number, and how to solve a two-step linear equation. Simplifying expressions When solving equations, you may need to simplify algebraic expressions as much as possible. For example: 3(5𝑥 + 1) simplifies to 3 ∙ 5𝑥 + 3 ∙ 1 and 10𝑥 − 3𝑥 simplifies to 7𝑥 We say that 3(5𝑥 + 1) is equivalent to 3 ∙ 5𝑥 + 3 ∙ 1, and 10𝑥 − 3𝑥 is equivalent to 7𝑥. 1) Which expressions are equivalent to the expression below? There may be more than one correct answer. 2(5𝑥 + 4) – 3𝑥 + 1 2) a) 10𝑥 + 8 – 3𝑥 + 1 b) 18𝑥 – 3𝑥 + 1 c) 15𝑥 + 1 d) 7𝑥 + 9 Which expressions are equivalent to the expression below? There may be more than one correct answer. −3(2𝑥 – 1) + 3(𝑥 + 1) − 4𝑥 a) −6𝑥 + 3 + 3𝑥 + 3 − 4𝑥 b) −10𝑥 + 6 + 3𝑥 c) −𝑥 + 12 d) 7𝑥 + 6 Foundations of Mathematical Reasoning Version 3.0 (2020) Student Pages Exponents It is important to pay careful attention to notation when working with negatives. For example, – 52 is not the same as (–5)2. You can verify this by evaluating each Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin expression on a calculator. The order of operations is the reas ...
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