Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
Cumulative Assessment

Exercise 5 Page 49

What can we 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. Let's organize our equations in a table.

Equation Solution
6x+6=- 14
5x+3=- 7
8x+6=- 2x-14
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 the first equation.

6x+6=- 14
6x=- 20
x = - 20/6
x = - 20/6
x = - 10/3

Following similar steps, we can solve each of the remaining equations. Let's summarize our findings in our table.

Equation Solution
6x+6=- 14 x= - 10/3
5x+3=- 7 x=- 2
8x+6=- 2x-14 x=- 2
7x+6=2x-13 x= - 19/5

Notice that 5x+3=- 7 and 8x+6=- 2x-14 have the same solution. Therefore, they are equivalent.