body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

Cumulative Assessment

Exercise 5 Page 49

What can you say about the solutions to two equivalent equations?

5x+3=- 7 and 8x+6=- 2x-14

Practice makes perfect

Recall that two linear equations are equivalent when you can get one from the other using the Properties of Equality. As a result, those linear equations have the same solution. First, let's name each of the given equations so they are easier to refer to.

Name	Equation
A	6x+6=- 14
B	5x+3=- 7
C	8x+6=- 2x-14
D	7x+6=2x-13

We will now solve each equation by isolating the variable to see if they have the same solutions. Let's start with Equation A.

6x+6=- 14

LHS-6=RHS-6

6x=- 20

.LHS /6.=.RHS /6.

x = - 20/6

MoveNegNumToFrac

Put minus sign in front of fraction

x = - 20/6

a/b=.a /2./.b /2.

x = - 10/3

Following similar steps, can solve each of the remaining equations. We will summarize our findings in a table.

Name	Equation	Solution
A	6x+6=- 14	x= - 10/3
B	5x+3=- 7	x=- 2
C	8x+6=- 2x-14	x=- 2
D	7x+6=2x-13	x= - 19/5

Notice that B and C have the same solution. Therefore, they are equivalent.

Subchapter links

Exercises p.48-49