Solving TwoStep Equations

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Solving Two-Step Equations

• Objective Solve equations that involve more than
  one operation.

2
5-Minute Check

• Rupesh earned some money mowing lawns one month.
  He put half of his money into savings. With the
  rest, he spent 15 on a new CD, 6 to see a
  movie, 3 on food, and he still had 24 left. How
  much money did Rupesh earn mowing lawns that
  month?

3
5-Minute Check

• Rupesh earned some money mowing lawns one month.
  He put half of his money into savings. With the
  rest, he spent 15 on a new CD, 6 to see a
  movie, 3 on food, and he still had 24 left. How
  much money did Rupesh earn mowing lawns that
  month?
• 96

4
5-Minute Check

• In an intramural basketball game, Annie made 6
  points more than Roberto. Roberto made half as
  many points as Charlie. Charlie made 3 more
  points than Darla. If Darla made 9 points, how
  many points did Annie make?

5
5-Minute Check

• In an intramural basketball game, Annie made 6
  points more than Roberto. Roberto made half as
  many points as Charlie. Charlie made 3 more
  points than Darla. If Darla made 9 points, how
  many points did Annie make?
• 12 points

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7-2 Solving Two-Step Equations
To solve two-step equations, first undo
operations involving numbers without variables.
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7-2 Solving Two-Step Equations
Example Solve b/2 8 20. Check your solution.
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7-2 Solving Two-Step Equations
Example Solve b/2 8 20. Check your
solution. b/2 8 20 b/2 8 8 20
8
Add 8 to each side.
9
7-2 Solving Two-Step Equations
Example Solve b/2 8 20. Check your
solution. b/2 8 20 b/2 8 8 20
8 b/2 28
Add 8 to each side.
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7-2 Solving Two-Step Equations
Example Solve b/2 8 20. Check your
solution. b/2 8 20 b/2 8 8 20
8 b/2 28 2 b/2 28 2
Add 8 to each side. Multiply each side by 2.
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7-2 Solving Two-Step Equations
Example Solve b/2 8 20. Check your
solution. b/2 8 20 b/2 8 8 20
8 b/2 28 2 b/2 28 2 b
56
Add 8 to each side. Multiply each side by 2.
12
7-2 Solving Two-Step Equations
Example Solve b/2 8 20. Check your
solution. b/2 8 20 b/2 8 8 20
8 b/2 28 2 b/2 28 2 b
56 Check b/2 8 20
Add 8 to each side. Multiply each side by 2.
13
7-2 Solving Two-Step Equations
Example Solve b/2 8 20. Check your
solution. b/2 8 20 b/2 8 8 20
8 b/2 28 2 b/2 28 2 b
56 Check b/2 8 20 56/2 8 ? 20

Add 8 to each side. Multiply each side by 2.
Replace b with 56.
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7-2 Solving Two-Step Equations
Example Solve b/2 8 20. Check your
solution. b/2 8 20 b/2 8 8 20
8 b/2 28 2 b/2 28 2 b
56 Check b/2 8 20 56/2 8 ? 20
28 8 ? 20
Add 8 to each side. Multiply each side by 2.
Replace b with 56. Do the division first.
15
7-2 Solving Two-Step Equations
Example Solve b/2 8 20. Check your
solution. b/2 8 20 b/2 8 8 20
8 b/2 28 2 b/2 28 2 b
56 Check b/2 8 20 56/2 8 ? 20
28 8 ? 20 20 ? 20
Add 8 to each side. Multiply each side by 2.
Replace b with 56. Do the division first. The
solution is 56.
16
7-2 Solving Two-Step Equations
Example Solve b/2 8 20. Check your
solution. b/2 8 20 b/2 8 8 20
8 b/2 28 2 b/2 28 2 b
56 Check b/2 8 20 56/2 8 ? 20
28 8 ? 20 20 ? 20
Add 8 to each side. Multiply each side by 2.
Replace b with 56. Do the division first. The
solution is 56.
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7-2 Solving Two-Step Equations
Application Solve the following by first writing
an equation. Teresas grocery bill totaled
12.5. If she bought an item for 7.94 and two
packs of soft drinks, how much did each pack of
soft drinks cost?
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7-2 Solving Two-Step Equations
Application Solve the following by first writing
an equation. Teresas grocery bill totaled
12.5. If she bought an item for 7.94 and two
packs of soft drinks, how much did each pack of
soft drinks cost? Answer 2.28