Cumulative Assessment
Sign In
What can we say about the solutions to two equivalent equations?
5x+3=- 7 and 8x+6=- 2x-14
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 |
LHS-6=RHS-6
.LHS /6.=.RHS /6.
Put minus sign in front of fraction
a/b=.a /2./.b /2.
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.