8.4 Solve Two-Step Equations
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
Solve the one-step equations.
1) x + 13 = 25
2) 15.1 = x − 4.3
3) 2x = 54
4)
x
= 14
3
Solve Two-Step Equations
As equations get more complicated do
we still use inverse operations on
both sides to get x by itself?
3x − 8 = 13
+8
+8
NOTES
The first step to solve a two-step equation is to get rid
of “the constant on the same side as x.”
Concept Check
Get rid of the constant on the same side as x.
2x + 6 = 20
29 = 4x + 1
26 = 6 + 5x
x
−7= 4
3
NOTES
The second step is to solve the one-step equation that
remains.
Examples
Solve the two-step equations.
3x − 5 = 7
x
7= −2
8
x
+3=9
4
18 = 2x + 4
EXAMPLES
Solve the equation.
x
2.6 = − 7.4
3
EXAMPLES
Two sides of a rectangle are both 4 inches. If the
perimeter is 30 inches, write and solve a two-step
equation to find the missing lengths.
L
4 in
4 in
L
PRACTICE
Solve the equations.
6x − 5 = 13
x
+ 13 = 18
9
31 = 7x − 53
x
3+ = 8
4
PRACTICE
Solve the equation.
2x − 7 = 18
15.3 = 4x − 12.7
FINAL QUESTION
Two sides of a rectangle are both 9 centimeters. If the
perimeter is 50 cm, write and solve a two-step equation
to find the missing lengths.
L
9 cm
9 cm
L