Page 29 - Math Course 1 (Book 2)

Solving Open Sentence Equations

Your Turn!
True or
a 4a + 7 = 23
False? Use a Replacement Set to Solve an Equation
2 4(2) + 7 ≟ 23 → 15 ≠ 23 false
3 4(3) + 7 ≟ 23 → 19 ≠ 23 false A. Find the solution set for 6c – 5 = 7 if the
4 4(4) + 7 ≟ 23 → 23 = 23 true ! replacement set is {0, 1, 2, 3, 4}.
5 4(5) + 7 ≟ 23 → 27 ≠ 23 false A. {0}
6 4(6) + 7 ≟ 23 → 31 ≠ 23 false B. {2}
C. {1}
D. {4}
Answer The solution set is {4}.

Answer

Find the solution set for 3(8 – b) = 6 if the replace-
ment set is {2, 3, 4, 5, 6}.

Replace b in 3(8 – b) = 6 with each value in the B. Find the solution set for 4(h – 2) = –8 if the
replacement set.
replacement set is {0, 1, 2, 3, 4}.
True or
a 3(8 – b) = 6 A. {1}
False?
B. {2}
2 3(8 – 2) ≟ 6 → 18 ≠ 6 false C. {0}
3 3(8 – 3) ≟ 6 → 15 ≠ 6 false D. {3}
4 3(8 – 4) ≟ 6 → 12 ≠ 6 false
5 3(8 – 5) ≟ 6 → 9 ≠ 6 false Answer
6 3(8 – 6) ≟ 6 → 6 = 6 true !

Answer The solution set is {6}.

Use Order of Operations to Solve an Equation Use Order of Operations to Solve an Equation
3(6 + 4) = w
Solve
Examples 21 – (10–6) 2

5(8 + 2) A. 1
Solve = k
18 – (5 – 3) 3 30
B.
5(8 + 2) 37
3
18 – (5 – 3) 3 = k Original equation C. 8

5(10) Add 8 and 2 in the D. 6
18 – (2) 3 = k numerator. Subtract 5
and 3 in the denominator
5(10)
18 – 8 = k Evaluate the power in the
denominator.
50 = k
10 Simplify
Answer
5 = k Divide.
Answer
The solution is 5.

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