Page 23 - Math Course 2 (Book 1)

Solving Algebraic Equations

To check your solution, replace x with –7 in the Read the test item.
original equation.
Translate the verbal sentence into an equation.
Check
x + 4 = –3 Write the equation. Solve the test item.
?
–7 + 4 = –3 Check to see whether this Words Movie A earned $38 million less than
sentence is true. Movie B earned.

–3 = –3 The sentence is true.
Variable Let B = amount Movie B earned.
The solution is –7. To graph, draw
Answer
a dot at –7 on a number line.
Equation 225 = B – 38
So the equation 225 = B – 38 or
B – 38 = 225 can be used to f nd
Answer
–9 –8 –7 –6 –5 –4 –3 –2 the amount Movie B earned. This
is choice D.

Solve Equations by Adding Real World Example

Example MOUNTAINS
Write and solve an equation to f nd the height of
Guadalupe Peak, the highest point in Texas. Driskill
Solve y – 3 = –14. Mountain, with a height of 535 feet, is the highest
point in the neighboring state of Louisiana. It is 8214
y – 3 = –14 Write the equation. feet lower than Guadalupe Peak.

y + (–3) = –14 Rewrite y – 3 as y + (–3). Let h = the height of Guadalupe Peak.

y + (–3) + 3 = 14 + 3 Add 3 to each side. 535 = h – 8214 Write the equation.

y + 0 = –14 + 3 Additive Inverse 535 + 8214 = h – 8214 + 8214 Add 8214 to each
Property; (–3) + 3 = 0 side.

y = –11 Identity Property; 8749 = h Simplify.
y + 0 = y

Guadalupe Peak is 8749 feet
The solution is –11. Answer
Answer high.
Check your solution.

Multiple-Choice Test Item
Your Turn!

Example Solve Equations by Subtracting

Solve y + 7 = 3. Check your solution.
ENTERTAINMENT
Movie A earned $225 million at the box of ce. That A. 10
is $38 million less than Movie B earned. Which B. 4
equation can be used to f nd the amount of money C. –4
Movie B earned? D. –10

A. B + 38 = 225 B. 38 – B = 225
C. B = 225 – 38 D. B – 38 = 225 Answer

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