25 Solving Equations with the Variable on Each Side

1
2-5 Solving Equations with the Variable on Each
Side
Please take a highlighter or red pencil and draw
a line through the equal signs for every homework
problem. Does it produce a straight line for
each problem?
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
2
STEPS FOR SOLVING LINEAR EQUATIONS
1. Simplify each side by distributing and/or
combining like terms.
2. Collect variable terms on the side where the
coefficient is greater.
3. Isolate the variable using inverse
operations.
4. Check your solution in the original equation.
3
Solve.
Write problem.
Change subtraction to addition.




Distribute and combine like terms.
Collect variable terms on one side.
Isolate the variable using inverse operations.
4
Solve.
Example 1
Example 2
5
Linear equations (equations that have a variable
to the first power) can have one solution, no
solution, or it is an identity and all numbers
are solutions.
The equation 2x 2x is called an identity.
One side is identical to the other side.
6
Solve the equation, if possible. Determine
whether it has one solution, no solution, or it
is an identity and thus all numbers are solutions.
one solution
no solution
all numbers
This type of equation is called an Identity! The
variable can represent all numbers.
True statement means all numbers are
solutions. False statement means no solution.
7
Solve the equation, if possible. Determine
whether it has one solution, no solution, or it
is an identity and thus all numbers are solutions.
Example 3
Example 4
Example 5
all numbers
no solution
8
Solve the equation, if possible. Determine
whether it has one solution, no solution, or it
is an identity and thus all numbers are solutions.
Example 6
Example 7
Example 8
no solution
all numbers
9
Example 9 Find the value of x so that the figures
have the same perimeter.
5x 1
x 4
2x
2x 5
x 9
P a b c
P 2l 2w
Write the perimeter formula for each geometric
figure. Substitute.
If perimeter is equal to perimeter then . . .
10
Homework
2-A10 Pages 101103 3134,3742,49 and PRACTICE
Wkbk. Page 14 1424. (Complete PRACTICE
Workbook problems on binder paper.)