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EXAMPLE 1. Solving Equations Using Algebra Tiles. Use algebra tiles to solve x + 2 = 4 . EXAMPLE 1. Solving Equations Using Algebra Tiles. Use algebra tiles to solve x + 2 = 4 . Step 1 Represent the equation using algebra tiles. EXAMPLE 1. Solving Equations Using Algebra Tiles.

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Example 1

EXAMPLE 1

Solving Equations Using Algebra Tiles

Use algebra tiles to solve x+ 2 = 4.


Example 1

EXAMPLE 1

Solving Equations Using Algebra Tiles

Use algebra tiles to solve x+ 2 = 4.

Step 1 Represent the equation using algebra tiles.


Example 1

EXAMPLE 1

Solving Equations Using Algebra Tiles

Use algebra tiles to solve x+ 2 = 4.

Step 1 Represent the equation using algebra tiles.

Step 2Take away two 1-tiles from each side.


Example 1

EXAMPLE 1

Solving Equations Using Algebra Tiles

Step 3 The remaining tiles show that the value of x

is 2.


Example 1

EXAMPLE 1

Solving Equations Using Algebra Tiles

Step 3 The remaining tiles show that the value of x

is 2.

ANSWER

The solution is 2.


Example 1

for Example 1

GUIDED PRACTICE

Use algebra tiles to solve the equation.


Example 1

for Example 1

GUIDED PRACTICE

Use algebra tiles to solve the equation.

1. x + 1 = 5


Example 1

for Example 1

GUIDED PRACTICE

Use algebra tiles to solve the equation.

1. x + 1 = 5

ANSWER

4


Example 1

for Example 1

GUIDED PRACTICE

2. x + 3 = 9


Example 1

for Example 1

GUIDED PRACTICE

2. x + 3 = 9

ANSWER

6


Example 1

for Example 1

GUIDED PRACTICE

3. 4+ x = 4


Example 1

for Example 1

GUIDED PRACTICE

3. 4+ x = 4

ANSWER

0


Example 1

for Example 1

GUIDED PRACTICE

4. 8 = 7 + x


Example 1

for Example 1

GUIDED PRACTICE

4. 8 = 7 + x

ANSWER

1


Example 1

EXAMPLE 2

Solving an Addition Equation

Solve the equation y + 25 = 140.


Example 1

EXAMPLE 2

Solving an Addition Equation

Solve the equation y + 25 = 140.

=

y + 25

140

Write the original equation.

– 25

– 25

Subtract 25 from each side.

.

y

=

115

Simplify.


Example 1

?

=

EXAMPLE 2

Solving an Addition Equation

Solve the equation y + 25 = 140.

=

y + 25

140

Write the original equation.

– 25

– 25

Subtract 25 from each side.

.

y

=

115

Simplify.

Check

y + 25

=

140

Write the original equation.

115 + 25

140

Substitute 115 for y.

140

=

140

Solution checks.


Example 1

EXAMPLE 3

Using an Addition Equation

Shopping

You buy an outfit at a vintage shop that costs $17.45. You pay with a $20 bill. What is the amount of change cthat the clerk should give you?


Example 1

EXAMPLE 3

Using an Addition Equation

Shopping

You buy an outfit at a vintage shop that costs $17.45. You pay with a $20 bill. What is the amount of change cthat the clerk should give you?

SOLUTION

Cost +Change

Amount paid

=

Write a verbal model.

17.45 + c

=

20.00

Write an equation.

– 17.45

– 17.45

=

Subtract 17.45 from each side.

.

c

2.55

=

Simplify.


Example 1

EXAMPLE 3

Using an Addition Equation

Shopping

You buy an outfit at a vintage shop that costs $17.45. You pay with a $20 bill. What is the amount of change cthat the clerk should give you?

SOLUTION

Cost +Change

Amount paid

=

Write a verbal model.

17.45 + c

=

20.00

Write an equation.

– 17.45

– 17.45

=

Subtract 17.45 from each side.

.

c

2.55

=

Simplify.

ANSWER

The clerk should give you $2.55 in change.


Example 1

for Examples 2 and 3

GUIDED PRACTICE

Solve the equation. Then check the solution.


Example 1

for Examples 2 and 3

GUIDED PRACTICE

Solve the equation. Then check the solution.

5. p + 24 = 88


Example 1

for Examples 2 and 3

GUIDED PRACTICE

Solve the equation. Then check the solution.

5. p + 24 = 88

ANSWER

64


Example 1

for Examples 2 and 3

GUIDED PRACTICE

6. 15 + q = 105


Example 1

for Examples 2 and 3

GUIDED PRACTICE

6. 15 + q = 105

ANSWER

90


Example 1

for Examples 2 and 3

GUIDED PRACTICE

7. 76 = r + 39


Example 1

for Examples 2 and 3

GUIDED PRACTICE

7. 76 = r + 39

ANSWER

37


Example 1

for Examples 2 and 3

GUIDED PRACTICE

8. s + 2.5 = 10.7


Example 1

for Examples 2 and 3

GUIDED PRACTICE

8. s + 2.5 = 10.7

ANSWER

8.2


Example 1

for Examples 2 and 3

GUIDED PRACTICE

9. 8.35 + t = 10.55


Example 1

for Examples 2 and 3

GUIDED PRACTICE

9. 8.35 + t = 10.55

ANSWER

2.20


Example 1

for Examples 2 and 3

GUIDED PRACTICE

10. u + 1.85 = 50


Example 1

for Examples 2 and 3

GUIDED PRACTICE

10. u + 1.85 = 50

ANSWER

48.15


Example 1

for Examples 2 and 3

GUIDED PRACTICE

Suppose the total cost in Example 3 is $23.65, and you give the clerk $25. How much change should you receive?

What If?

11.

ANSWER

$1.35


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