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Chapter 2 2.1 Exercises
18.
16 x + 5 = 10 x − 1 16 x − 10 x + 5 = 10 x − 10 x − 1 6 x + 5 = −1 6 x + 5 − 5 = −1 − 5 6 x = −6 6 x −6 = 6 6 x = −1 Check: 16(−1) + 5 ⱨ 10(−1) − 1 −16 + 5 ⱨ − 10 − 1 −11 = −11
20.
−11x − 8 = 2 x + 5 −11x − 2 x − 8 = 2 x − 2 x + 5 −13x − 8 = 5 −13x − 8 + 8 = 5 + 8 −13x = 13 −13x 13 = −13 −13 x = −1 Check: −11(−1) − 8 ⱨ 2(−1) + 5 11 − 8 ⱨ − 2 + 5 3=3
22.
6a + 5 − a = 3a − 9 5a + 5 = 3a − 9 5a − 3a + 5 = 3a − 3a − 9 2 a + 5 = −9 2 a + 5 − 5 = −9 − 5 2a = −14 2a −14 = 2 2 a = −7 Check: 6(−7) + 5 − (−7) ⱨ 3(−7) − 9 −42 + 5 + 7 ⱨ − 21 − 9 −30 = −30
24.
3(5 − y) = 3( y + 4) 15 − 3 y = 3 y + 12 15 − 3 y − 3 y = 3 y − 3 y + 12 15 − 6 y = 12 15 − 15 − 6 y = 12 − 15 −6 y = −3 −6 y −3 = −6 −6 1 y = or 0.5 2
2. 2 x + 12 = 2(21) + 12 = 54 ≠ −30 No; 21 is not a root since replacing x with 21 does not give a true statement.
⎛3⎞ 4. 5 y + 9 = 5 ⎜ ⎟ + 9 = 3 + 9 = 12 ⎝5⎠ 3 Yes: when you replace y by in the equation, 5 you get a true statement. 6. Multiply each term of the equation by 100 to clear the decimals.
1 to both sides of 4 the equation since the coefficient of x is 1.
8. No; it would be easier to add
10.
26 + x = −35 26 + x − 26 = −35 − 26 x = −61 Check: 26 + (−61) ⱨ − 35 −35 = −35
12. −16 x = −64 −16 x −64 = −16 −16 x=4 Check: −16(4) ⱨ − 64 −64 = −64 14. −15 x = 75 −15 x 75 = −15 −15 x = −5 Check: −15(−5) ⱨ 75 75 = 75 16.
10 x + 3 = 15 10 x + 3 − 3 = 15 − 3 10 x = 12 10 x 12 = 10 10 6 1 x = or 1 or 1.2 5 5 ⎛6⎞ Check: 10 ⎜ ⎟ + 3 ⱨ 15 ⎝5⎠ 15 = 15
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