1. Algebra 1 Glencoe McGraw-Hill JoAnn Evans
Solving Equations
With Variables on Both Sides
&
Special Cases
Algebra Glencoe McGraw-Hill JoAnn Evans

2. But it works this way too.
Some equations have variables on both sides of the equal sign. To solve such equations, collect like variables on the same side.
In the equation shown below, the term 9x has a greater coefficient than the term 4x. You can avoid a negative coefficient by collecting variables on the right.
But it works this way too.

3. Solve the equation by collecting like variables on one side
Solve the equation by collecting like variables on one side. Check the solution.

4. Solve the equation by collecting like variables on one side
Solve the equation by collecting like variables on one side. Check the solution.

5. Check the solution with mental math.
Solve the equation by collecting like variables on one side. Check the solution.
Check the solution with mental math.

6. Try this one on your own:
Don’t be reluctant to check a fractional solution It’s just arithmetic!

7. commutative property of addition
A special type of equation
commutative property of addition
When you try to solve an identity, you end up with a statement that is always true.
When the two sides of an equation are identical it’s called an identity. What happens if you continue solving?

8. INFINITELY MANY SOLUTIONS.
An identity will have
INFINITELY MANY SOLUTIONS.
When the two sides of an equation are identical, any number substituted in as a solution will make a true statement.
All real numbers are solutions of an identity.
Write: All Real Numbers

9. Another special type of equation
Untrue statement!
When all variable terms cancel out and what’s left is an untrue statement of equality, there is no solution to the equation.
Write: No Solution

10. It is an identity. All real numbers are solutions of this equation.
Solve the equation, if possible. Determine whether it has one solution, no solution, or is an identity and thus all real numbers are solutions.
It is an identity. All real numbers are solutions of this equation.

11. An untrue statement is left, so there is
no solution to this equation. No value of the variable will make the equation true.
This equation has one solution.
x = -10

12. One solution!

13. No solution!
All real numbers!

14. Extra practice problems: