1-4 Solving Absolute Value Equations
Evaluate each expression if a = –3, b = –5, and
c = 4.2.
19. SOLUTION: Substitute –3 for a and 4.2 for c and solve.
14. SOLUTION: Substitute 4.2 for c and solve.
15. 20. SOLUTION: Substitute –5 for b and solve.
SOLUTION: Substitute –3 for a and 4.2 for c and solve.
16. SOLUTION: Substitute –3 for a and –5 for b and solve.
17. SOLUTION: Substitute –5 for b and 4.2 for c and solve.
21. SOLUTION: 22. FOOD To make cocoa powder, cocoa beans are
roasted. The ideal temperature for roasting is 300°F, plus or minus 25°. Write and solve an equation describing the maximum and minimum roasting
temperatures for cocoa beans.
SOLUTION: Solve the equation
.
18. SOLUTION: Substitute –3 for a and –5 for b and solve.
So, the maximum temperature is 325°F and the
minimum temperature is 275°F.
Solve each equation. Check your solutions.
23. SOLUTION: 19. SOLUTION: eSolutions
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Substitute –3 for a and 4.2 for c and solve.
Page 1
The solution set is
1-4 Solving
Absolutetemperature
Value Equations
So, the maximum
is 325°F and the
minimum temperature is 275°F.
Solve each equation. Check your solutions.
.
25. 23. SOLUTION: SOLUTION: There appear to be two solutions, 4 and –14.
Check: Substitute each value in the original equation.
There appear to be two solutions, 34 and –8.
Check: Substitute each value in the original equation.
The solution set is
The solution set is
.
.
26. 24. SOLUTION: SOLUTION: There appear to be two solutions, 41 and –29.
Check: Substitute each value in the original equation.
There appear to be two solutions, 8 and –26.
The solution set is
The solution set is
.
.
27. 25. SOLUTION: eSolutions
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There appear to be two solutions, 4 and –14.
Check: Substitute each value in the original equation.
SOLUTION: Page 2
1-4 Solving
Absolute Value Equations
The solution set is
.
27. The solution set is
.
28. SOLUTION: SOLUTION: There appear to be two solutions, –2 and –10.
Check: Substitute each value in the original equation.
There appear to be two solutions, 3 and –11.
Check: Substitute each value in the original equation.
The solution set is
The solution set is
.
.
29. 28. SOLUTION: SOLUTION: There appear to be two solutions, 3 and –11.
Check: Substitute each value in the original equation.
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Check: Substitute a = 2 in the original equation.
Page 3
1-4 Solving
Absolute Value Equations
The solution set is
.
29. The solution is a = 2.
30. SOLUTION: SOLUTION: Check: Substitute a = 2 in the original equation.
Check:
The solution is a = 2.
30. The solution is
.
SOLUTION: 31. SOLUTION: Check:
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Since 10 ≠ 6, the solution set is 1-4 Solving
Absolute
The solution
is . Value Equations
.
32. SOLUTION: 31. SOLUTION: There appear to be two solutions,
.
Check: Substitute the values in the original equation.
There appear to be two solutions,
.
Check: Substitute each value in the original equation.
Since 10 ≠ 6, the solution set is .
32. SOLUTION: The solution set is
.
33. eSolutions Manual - Powered by Cognero
SOLUTION: Page 5
The solution set is
.
1-4 Solving Absolute Value Equations
33. SOLUTION: Since −6 ≠ 6, the solution set is .
34. SOLUTION: There appear to be two solutions,
.
Check: Substitute the values in the original equation.
There appear to be two solutions,
.
Check: Substitute the values in the original equation.
z=
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There appear to be two solutions,
.
Check: Substitute the values in the original equation.
1-4 Solving
Absolute Value Equations
z=
The solution set is
.
Solve each equation. Check your solution.
57. SOLUTION: z=
Check: Substitute p = –2 in the original equation.
The solution is p = –2.
59. MONEY Nhu is saving to buy a car. In the first 6
The solution set is
months, his savings were $80 less than
.
Solve each equation. Check your solution.
57. SOLUTION: the price of the car. In the second six months, Nhu saved $50
more than
the price of the car. He still needs $370.
a. What is the price of the car?
b. What is the average amount of money Nhu saved
each month?
c. If Nhu continues to save the average amount each
month, in how many months will he be able to afford
the car?
SOLUTION: a. Let x (in dollars) be the price of the car.
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Page 7
month, in how many months will he be able to afford
the car?
SOLUTION: 1-4 Solving Absolute Value Equations
a. Let x (in dollars) be the price of the car.
Distributive Property; the Distributive Property states
that there is no difference between a term multiplied
by each term in a group and the term multiplied by
the group.
Simplify each expression.
63. 3x + 5y + 7x – 3y
SOLUTION: 65. 2(10m – 7a) + 3(8a – 3m)
SOLUTION: 67. 4(14c – 10d) – 6(d + 4c)
SOLUTION: The price of the car is $6800.
b. $6800 − $370 = $6430
So, Nhu saved $6430 in 12 months.
The average amount of money Nhu saved each
month is about $535.83.
c. Since $6430 + $535.83 > $6800, he will be able to
afford the car in 1 month.
Name the property illustrated by each equation.
61. SOLUTION: Distributive Property; the Distributive Property states
that there is no difference between a term multiplied
by each term in a group and the term multiplied by
the group.
Simplify each expression.
+ 5y + 7x – 3y
63. 3x
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SOLUTION: Page 8