Beyond Boundaries: Leveraging No-Code Solutions for Industry Innovation
3.4 solve equations with variables on both sides day 2
1. When an equation has variables on both sides,
some different things can happen.
Look at this equation:
x+2=4+x
Why does this look strange?
2. 3x - 9 = 3x + 10
2(3x + 4) = 6x + 9
A linear equation has NO SOLUTION when
the solved equation has no variable and the
equation is false.
3. When an equation has variables on both sides,
something else may occur. Look at this
example:
4(x – 5) = 4x - 20
What numbers make this sentence true?
4. 2(6 + 3x) = 6x + 12
This is also called “identity”. It means ALL
REAL NUMBERS make the sentence true.
A linear equation is an identity when the solved
equation has NO VARIABLE and the solution
is TRUE!
5. When solving equations with variables on
both sides, 3 different things can happen.
1) solution is a single number ( x = 4)
2) solution is ALL REALS ( IDENTITY)
3) solution is NO SOLUTION (empty set)
6. Cont’ P. 157 (#18-28)
Show ALL STEPS!!
Mentally check solutions
Watch for “Identity” and “No Solution”
equations.
