Download 1-3 Solving Equations p22 23-57 odd 63

1-3 Solving Equations
Write an algebraic expression to represent each verbal expression.
23. the product of the square of a number and 8
SOLUTION: Let the number be x.
2
The square of x is x .
2
The algebraic expression is 8x .
25. five more than the quotient of a number and 4
SOLUTION: Let the number be x. The quotient of x and 4 is
Five more than
.
is +5.
Write a verbal sentence to represent each equation.
27. SOLUTION: The quotient of the sum of 3 and a number and 4 is 5.
29. BASEBALL During a recent season, Miguel Cabrera and Mike Jacobs of the Florida Marlins hit a combined total
of 46 home runs. Cabrera hit 6 more home runs than Jacobs. How many home runs did each player hit? Define a
variable, write an equation, and solve the problem.
SOLUTION: n = number of home runs Jacobs hit.
Cabrera hit 6 more home runs than Jacobs. The keyword ‘more than’ mean addition.
So, number of home runs Cabrera hit = n + 6.
Total number of home runs is 46.
Therefore:
Jacobs hit 20 home runs and Cabrera hit 26 home runs.
Name the property illustrated by each statement.
31. If y = –3, then 7y = 7(–3)
SOLUTION: Substitution Property of Equality; the Substitution Property of Equality states that if a = b, then a may be replaced by
b and b may be replaced by a.
33. If –y = 13, then –(–y) = –13
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SOLUTION: Multiplication Property of Equality; this states that for any real numbers a, b, and c,
.
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, if a = b, then
31. If y = –3, then 7y = 7(–3)
SOLUTION: Substitution Property of Equality; the Substitution Property of Equality states that if a = b, then a may be replaced by
1-3 Solving
b and b Equations
may be replaced by a.
33. If –y = 13, then –(–y) = –13
SOLUTION: Multiplication Property of Equality; this states that for any real numbers a, b, and c,
.
, if a = b, then
Solve each equation. Check your solution.
35. SOLUTION: Substitute y = 5 in the original equation.
The solution is y = 5.
37. SOLUTION: Substitute y = –3 in the equation.
The solution is y = –3.
39. SOLUTION: Substitute x = –6 in the equation.
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1-3 Solving Equations
The solution is y = –3.
39. SOLUTION: Substitute x = –6 in the equation.
The solution is x = –6.
41. SOLUTION: Substitute c = –3 in the equation.
The solution is c = –18.
43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side.
SOLUTION: The perimeter of a regular pentagon is given by P = 5s, where s is the side length.
Substitute P = 100.
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The length of each side of the pentagon is 20 inches.
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1-3 Solving Equations
The solution is c = –18.
43. GEOMETRY The perimeter of a regular pentagon is 100 inches. Find the length of each side.
SOLUTION: The perimeter of a regular pentagon is given by P = 5s, where s is the side length.
Substitute P = 100.
The length of each side of the pentagon is 20 inches.
Solve each equation. Check your solution.
55. SOLUTION: Check:
The solution is k = −4.
57. SOLUTION: Check:
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1-3 Solving
Equations
The solution
is k = −4.
57. SOLUTION: Check:
The solution is
.
63. CHALLENGE Solve
for y 1
SOLUTION: 65. OPEN ENDED Provide one example of an equation involving the Distributive Property that has no solution and
another example that has infinitely many solutions.
SOLUTION: Sample answer:
3(x – 4) = 3x + 5 This has no solution since it simplifies to an untrue equation.
2(3x – 1) = 6x – 2 This has infinite number of solutions since it simplifies to a true equation and x can be any real
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number.
67. The graph shows the solution of which inequality?
1-3 Solving Equations
65. OPEN ENDED Provide one example of an equation involving the Distributive Property that has no solution and
another example that has infinitely many solutions.
SOLUTION: Sample answer:
3(x – 4) = 3x + 5 This has no solution since it simplifies to an untrue equation.
2(3x – 1) = 6x – 2 This has infinite number of solutions since it simplifies to a true equation and x can be any real
number.
67. The graph shows the solution of which inequality?
A.
C. B.
D. SOLUTION: The slope of the line is
and the y-intercept is 4. So, the equation corresponding to the inequality is
Since the upper region of the line is shaded, the inequality is
69. GEOMETRY Which of the following describes the transformation of
.
. So, the correct choice is D.
to
?
A. a reflection across the y-axis and a translation down 2 units
B. a reflection across the x-axis and a translation down 2 units
C. a rotation
to the right and a translation down 2 units
D. a rotation
to the right and a translation right 2 units
SOLUTION: Analyzing the graph shows that the image was reflected across the y-axis. The answer is A a reflection across the
y-axis and a translation down 2 units.
71. Simplify
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.
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SOLUTION: Analyzing
the graph shows that the image was reflected across the y-axis. The answer is A a reflection across the
1-3 Solving
Equations
y-axis and a translation down 2 units.
71. Simplify
.
SOLUTION: 73. LANDMARKS Suppose the Space Needle in Seattle, Washington, casts a 220-foot shadow at the same time a
nearby tourist casts a 2-foot shadow. If the tourist is
feet tall, how tall is the Space Needle?
SOLUTION: Let h be the height of the Space Needle.
The height of the Space Needle is 605 feet.
Identify the additive inverse for each number or expression.
75. SOLUTION: Since
, the additive inverse of
is .
77. SOLUTION: Since (–2x) + 2x = 0, the additive inverse of –2x is 2x.
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Since Equations
1-3 Solving
is , the additive inverse of
.
77. SOLUTION: Since (–2x) + 2x = 0, the additive inverse of –2x is 2x.
79. SOLUTION: Since
, the additive inverse of
is
.
81. SOLUTION: Since 5x – 5x = 0, the additive inverse of 5x is –5x.
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