x + 4 = 18
Solve the equation by working backward.
Since x + 4 = 18, then x = 18 – 4. So, x = 14.
If the sum of a number and four is equal to 18, the
Inquiry Lab: Solve One-Step Addition and Subtraction Equations
number is 14.
Solve the problem.
1. Draw a bar diagram and write an addition equation
to represent the
following situation. Then solve the equation.
The sum of a number and four is equal to 18.
Equation: __________ Solution: x = __________
SOLUTION: Draw a bar diagram representing the sentence. Let x
represent the number. The entire bar is 18. One
section is 4, and the other section is x.
Write an equation from the bar diagram.
x + 4 = 18
Solve the equation by working backward.
Since x + 4 = 18, then x = 18 – 4. So, x = 14.
If the sum of a number and four is equal to 18, the
number is 14.
2. Use Math Tools Jack collects postage stamps. He
sold 7 of his stamps and had 29 stamps left.
Complete the bar diagram below. Then write and
solve a subtraction equation to find the number of
stamps Jack had at the beginning.
Equation: __________ Solution: n = __________
So, Jack had
stamps at the beginning.
SOLUTION: Draw a bar diagram representing the sentence. Let n
represent the number of postage stamps which
represents the entire bar. One section should
represent the number of stamps sold, 7, and the other
section should represent the number of stamps left,
29.
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Write a subtraction equation from the bar diagram.
2. Use Math Tools Jack collects postage stamps. He
sold 7 of his stamps and had 29 stamps left.
Complete the bar diagram below. Then write and
solve a subtraction equation to find the number of
stamps Jack had at the beginning.
Equation: __________ Solution: n = __________
So, Jack had
stamps at the beginning.
SOLUTION: Draw a bar diagram representing the sentence. Let n
represent the number of postage stamps which
represents the entire bar. One section should
represent the number of stamps sold, 7, and the other
section should represent the number of stamps left,
29.
Write a subtraction equation from the bar diagram.
n – 7 = 29
Solve the equation by working backward.
Since n – 7 = 29, then n = 29 + 7. So, n = 36.
So, Jack had 36 stamps at the beginning.
3. Suppose Jack sold 15 stamps and had 21 stamps left.
How would the bar diagram change?
SOLUTION: Sample answer: Since Jack sold 15 stamps instead of
7, the stamps sold bar would be longer. He had 21
stamps left, therefore the number of stamps left bar
would be shorter.
4. Reason Abstractly Suppose Jack had 40 stamps in
the beginning and sold 7 of them. How would the bar
diagram change? What equation could you write to
represent the situation?
SOLUTION: Sample answer: Draw a bar diagram representing the sentence.
Label the entire bar diagram length as 40 since he
had 40 stamps in the beginning. The number of
stamps sold is still 7, so label the one section 7. The
other section would represent the number of stamps
Page 1
left, which is the unknown. Use n to represent the
number of stamps left.
Write an equation from the bar diagram.
SOLUTION: Sample answer: Since Jack sold 15 stamps instead of
There are no 1-tiles remaining on the right side of the
7, the stamps sold bar would be longer. He had 21
mat.
stamps
left,
therefore
the number
of stamps
left bar
Inquiry
Lab:
Solve
One-Step
Addition
and Subtraction
Equations
Therefore, x = 0.
would be shorter.
4. Reason Abstractly Suppose Jack had 40 stamps in
the beginning and sold 7 of them. How would the bar
diagram change? What equation could you write to
represent the situation?
SOLUTION: Sample answer: Draw a bar diagram representing the sentence.
Label the entire bar diagram length as 40 since he
had 40 stamps in the beginning. The number of
stamps sold is still 7, so label the one section 7. The
other section would represent the number of stamps
left, which is the unknown. Use n to represent the
number of stamps left.
Write an equation from the bar diagram.
7 + n = 40
6. –2 = x + 1
x = _____
SOLUTION: Model the equation.
Place two −1-tiles on the left side of the mat. Place
one x-tile and one 1-tile on the right side of the mat.
Add one −1-tile to the left side of the mat and add
one −1-tile to the right side of the mat to form a zero
pair on the right.
Use Math Tools Solve the equation. Use
algebra tiles. Show your work using drawings.
5. x + 4 = 4
x = _____
Remove the zero pair from the right side. There are
three −1-tiles on the left side of the mat.
Therefore, x = –3.
7. x – 1 = –3
x = _____
SOLUTION: Model the equation.
Place one x-tile and four 1-tiles on the left side of the
mat. Place four 1-tiles on the right side of the mat.
Remove four 1-tiles from each side of the mat so
that the variable is by itself on the left side.
There are no 1-tiles remaining on the right side of the
mat.
Therefore, x = 0.
SOLUTION: Model the equation.
Place one x-tile and one −1-tile on the left side of the
mat. Place three −1-tiles on the right side of the mat.
Add one 1-tile to the left side of the mat and add one
1-tile to the right side of the mat to form a zero pair
on the left. Identify the zero pair that is formed on
the right side of the mat.
6. –2 = x + 1
x = _____
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Remove the zero pair from each side. There arePage
two 2
−1-tiles on the right side of the mat.
Therefore, x = –2.
Remove the zero pair from the right side. There are
Remove the zero pair from each side. There are two
threeLab:
on One-Step
the left sideAddition
of the mat.
Inquiry
Solve
and Subtraction Equations
−1-tiles on the right side of the mat.
−1-tiles
Therefore, x = –3.
Therefore, x = –2.
7. x – 1 = –3
x = _____
8. 4 = x – 2
x = _____
SOLUTION: Model the equation.
Place one x-tile and one −1-tile on the left side of the
mat. Place three −1-tiles on the right side of the mat.
Add one 1-tile to the left side of the mat and add one
1-tile to the right side of the mat to form a zero pair
on the left. Identify the zero pair that is formed on
the right side of the mat.
SOLUTION: Model the equation.
Place four 1-tiles on the left side of the mat. Place
one x-tile and two −1-tiles on the right side of the
mat.
Add two 1-tiles to the right side of the mat and add
two 1-tiles to the left side of the mat to form zero
pairs on the right.
Remove the zero pair from each side. There are two
−1-tiles on the right side of the mat.
Therefore, x = –2.
Remove the zero pairs from the right side. There are
six 1-tiles on the left side of the mat.
Therefore, x = 6.
Complete the table. The first one is done for
you.
8. 4 = x – 2
x = _____
9. SOLUTION: Model the equation.
Place four 1-tiles on the left side of the mat. Place
one x-tile and two −1-tiles on the right side of the
mat.
Add two 1-tiles to the right side of the mat and add
two 1-tiles to the left side of the mat to form zero
pairs on the right.
SOLUTION: To solve an equation like 6 + x = 10, you “undo” the
last operation that was applied to the variable and
continue to “undo” operations in reverse order until
the value of the unknown is determined. In the case
of 6 + x = 10, the last operation applied to the
variable x is adding 6. To undo adding 6, you would
subtract 6 from each side. So, in general, if a number
is added to the variable, subtract that number from
both sides of the equation. So, the related equation
would be x = 10 – 6.
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Remove the zero pairs from the right side. There are
six 1-tiles on the left side of the mat.
Therefore, x = 6.
Page 3
Remove the zero pairs from the right side. There are
six 1-tiles
the One-Step
left side ofAddition
the mat. and Subtraction Equations
Inquiry
Lab: on
Solve
Therefore, x = 6.
Complete the table. The first one is done for
you.
10. 9. SOLUTION: To solve an equation like x + 3 = –1, you “undo” the
last operation that was applied to the variable and
continue to “undo” operations in reverse order until
the value of the unknown is determined. In the case
of x + 3 = –1, the last operation applied to the
variable x is adding 3. To undo adding 3, you would
subtract 3 from each side. So, in general, if a number
is added to the variable, subtract that number from
both sides of the equation. So, the related equation
would be x = –1 – 3.
SOLUTION: To solve an equation like 6 + x = 10, you “undo” the
last operation that was applied to the variable and
continue to “undo” operations in reverse order until
the value of the unknown is determined. In the case
of 6 + x = 10, the last operation applied to the
variable x is adding 6. To undo adding 6, you would
subtract 6 from each side. So, in general, if a number
is added to the variable, subtract that number from
both sides of the equation. So, the related equation
would be x = 10 – 6.
11. 10. SOLUTION: To solve an equation like x + 3 = –1, you “undo” the
last operation that was applied to the variable and
continue to “undo” operations in reverse order until
the value of the unknown is determined. In the case
of x + 3 = –1, the last operation applied to the
variable x is adding 3. To undo adding 3, you would
subtract 3 from each side. So, in general, if a number
is added to the variable, subtract that number from
both sides of the equation. So, the related equation
would be x = –1 – 3.
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SOLUTION: To solve an equation like 6 + x = –7, you “undo” the
last operation that was applied to the variable and
continue to “undo” operations in reverse order until
the value of the unknown is determined. In the case
of 6 + x = –7, the last operation applied to the
variable x is adding 6. To undo adding 6, you would
subtract 6 from each side. So, in general, if a number
is added to the variable, subtract that number from
both sides of the equation. So, the related equation
would be x = –7 – 6.
12. Construct an Argument Write a rule that you can
use to solve addition equations without using models
Page 4
or a drawing.
SOLUTION: Inquiry Lab: Solve One-Step Addition and Subtraction Equations
12. Construct an Argument Write a rule that you can
use to solve addition equations without using models
or a drawing.
SOLUTION: To solve an equation like x + 3 = 2, you “undo” the
last operation that was applied to the variable and
continue to “undo” operations in reverse order until
the value of the unknown is determined. In the case
of x + 3 = 2, the last operation applied to the variable
x is adding 3. To undo adding 3, you would subtract 3
from each side. So, in general, if a number is added
to the variable, subtract that number from both sides
of the equation.
13. HOW can bar diagrams or algebra tiles help you
solve an equation?
SOLUTION: Sample answer: A bar diagram or an algebra tile
model provides a visual aid when deciding which
operation to use.
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