9.2 Solve Equations by Combining
Like Terms
Common Core Standards
8. EE.7. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution,
infinitely many solutions, or no solutions. Show which of these
possibilities is the case by successively transforming the given
equation into simpler forms, until an equivalent equation of the form x =
a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including
equations whose solutions require expanding expressions using the
distributive property and collecting like terms.
WARM-UP
Simplify the expressions by combining like terms.
1) 7x + x − 9
2) 9x + 8 + 3x − 2
3) −2x + 8x − 6 + 9
4)
5x − 1 − 7x + 4
Solve Equations by Combining Like
Terms
As equations get more complicated how
do we make them simpler?
3x + 2x + 7 − 2 = 15
NOTES
One way to simplify equations is to combine the like
terms. Remember an operation is linked to the term that
follows it.
Concept Check
Simplify the equation by combining the like terms.
2x + 5x + 6 − 1 = 19
−3x − 7 + 2x + 9 = 5
29 = 4x + 1 − x + 10
EXAMPLES
Solve the equations.
9x + 5 + x − 2 = 23
20 = 4x − 3 + 2x + 5
EXAMPLES
Solve the equations.
−4x + 5 − x − 2 = 28
50 = 5x − 3 − 8x − 7
EXAMPLES
Find x if the perimeter is 30.
x
x+3
2x − 1
EXAMPLES
Which equation is equivalent?
−7x + 5 + 2x − 9 = 8 + 3
a) − 5x + 14 = 11
b) − 5x − 4 = 11
PRACTICE
Solve the equations.
7x + 5 − x + 6 = 53
13 = −8x + 9 + 5x − 8
PRACTICE
Find x if the perimeter is 40.
2x − 1
x+9
x
FINAL QUESTION
Which equation is equivalent?
4 + 20 = −3x + 8x − 11 + 5
24 = −5x − 6
24 = −5x − 16