Lesson 6
Solving Multi-Step Equations
Solve each equation.
1.
30 = 4x + 10
2.
x
 12   15
9
3.
0.7x – 2.1 = 0
Target:
Simplify and solve multi-step equations.
1.
Simplify each side of the equation by distributing and
combining like terms, when necessary.
2.
If variables are on both sides of the equation, balance
the equation by moving one variable term to the
opposite side of the equals sign using inverse
operations.
3.
Follow the process for solving one- and two-step
equations to get the variable by itself.
Solve the equation for x.
4(2x – 7) = 20
8x – 28 = 20
+ 28 + 28
8x = 48
8
8
x=6
4(2 ∙ 6 – 7) = 4(12 – 7) = 4(5) = 20
Solve the equation for x.
– 2x + 9 = 4x – 15
+ 2x
+ 2x
9 = 6x – 15
+ 15
+ 15
24 = 6x
6 6
4=x
?
– 2(4) + 9 = 4(4) – 15
– 8 + 9 = 16 – 15
1=1
Solve the equation for x.
5(x + 8) = – 2(x – 13)
5x + 40 = – 2x + 26
+ 2x
+ 2x
7x + 40 = 26
– 40 – 40
7x = –14
7
7
x=–2
?
5(– 2 + 8) = – 2(– 2 – 13)
5(6) = – 2(– 15)
30 = 30
Katie opened a coffee cart to earn some extra money. Her
one-time equipment start-up cost was $460. It costs her $1 to
make each cup of coffee. She plans to sell the cups of coffee
for $3. How many cups will she need to sell before she breaks
even?
460 + 1x = 3x
– 1x – 1x
460 = 2x
2
2
230 = x
Katie must sell 230 cups of coffee to break even.
Solve each equation.
1.
90 = 10(x + 7)
2.
6x − 13 = 4x + 11
3.
2(x − 9) = 3(x − 5)
Describe the process of solving a multi-step equation.