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Big Ideas Math: Modeling Real Life, Grade 7

BI

Big Ideas Math: Modeling Real Life, Grade 7 View details

1. Algebraic Expressions

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Exercise 8 Page 95

Start by simplifying the algebraic expression.

Yes, see solution.

Practice makes perfect

We want to determine whether the given algebraic expressions are equivalent. Let's start by looking at the expressions!

	Expression 1	Expression 2
Expression	1.25x+4+0.75x-3	2x+1
Terms
Like Terms

First, we will rewrite each expression as a sum of terms.

	Expression 1	Expression 2
Expression	1.25x+4+0.75x-3=1.25x+4+0.75x+(- 3)	2x+1
Terms
Like Terms

Next, we can identify the terms and like terms in each expression.

	Expression 1	Expression 2
Expression	1.25x+4+0.75x-3= 1.25x+ 4+ 0.75x+( - 3)	2x+ 1
Terms	1.25x, 4, 0.75x, - 3	2x, 1
Like Terms	1.25x and 0.75x, 4 and - 3	2x, 1

Looking at the table, we can see that we can simplify Expression 1. Let's group the like terms using the Commutative Property of Addition.

1.25x+4+0.75x+(- 3)

CommutativePropAdd

Commutative Property of Addition

1.25x+0.75x+4+(- 3)

Factor out x

(1.25+0.75)x+4+(- 3)

Add terms

2x+1

Notice that Expression 1 in simplest form has two terms, 2x and 1. We can see that the terms are the same as the terms in Expression 2. This means that Expression 1 is equivalent to Expression 2!

Subchapter links

Try It p.92-93

Self-Assessment for Concept & Skills p.93

Self-Assessment for Problem Solving p.94

Review & Refresh p.95

Concept, Skills, & Problem Solving p.95-96