Download Solve each equation. Check your solution. 11. 2m − 13 = −8 m + 27

 2-4 Solving Equations with the Variable on Each Side
Solve each equation. Check your solution.
11. 2m − 13 = −8m + 27
15. SOLUTION: SOLUTION: Check:
Check:
13. 6 + 3t = 8t − 14
SOLUTION: 17. 6(n + 5) = 66
SOLUTION: Check:
Check:
15. SOLUTION: 19. SOLUTION: eSolutions Manual - Powered by Cognero
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2-4 Solving Equations with the Variable on Each Side
22. GEOMETRY Find the value of x so the rectangles
have the same area.
19. SOLUTION: SOLUTION: The following is an expression for the area of the left
rectangle.
Check:
The following is an expression for the area of the
right rectangle.
21. 6(3a + 1) − 30 = 3(2a − 4)
SOLUTION: Set the expressions equal to each other and solve for
x.
Check:
Find the areas to check the solution.
22. GEOMETRY Find the value of x so the rectangles
have the same area.
23. NUMBER THEORY Four times the lesser of two
consecutive even integers is 12 less than twice the
greater number. Find the integers.
SOLUTION: eSolutions
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The Manual
following
is anby
expression
rectangle.
When x = 8, both figures have an area of 96 square units.
for the area of the left
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SOLUTION: Let x be the first even integer and x + 2 be the next
consecutive even integer.
x + 2 = −27 + 2 or −25
x + 4 = −27 + 4 or −23
So, the consecutive odd integers are −27, −25, and
−23.
When x = 8, both figures have an area of 96 square 2-4 Solving
Equations with the Variable on Each Side
units.
23. NUMBER THEORY Four times the lesser of two
consecutive even integers is 12 less than twice the
greater number. Find the integers.
Solve each equation. Check your solution.
25. 2x = 2(x − 3)
SOLUTION: SOLUTION: Let x be the first even integer and x + 2 be the next
consecutive even integer.
Since
, this equation has no solutions. To
check, substitute any number for x.
Check:
Substitute −4 into each expression to find the even
numbers.
x = −4
x + 2 = −4 + 2 or −2
So, the consecutive even integers are −4 and −2.
27. −5(3 − q) + 4 = 5q − 11
SOLUTION: 24. CCSS SENSE-MAKING Two times the least of
three consecutive odd integers exceeds three times
the greatest by 15. What are the integers?
SOLUTION: Let x = the least odd integer. Then x + 2 = the next
greater odd integer, and x + 4 = the greatest of the
three integers.
Since the expressions on each side are the same, the
equation is an identity. So, all numbers will work in
this equation. To check, substitute any number for q.
Check:
29. Substitute −27 into each expression to find the odd
numbers.
SOLUTION: x = −27
x + 2 = −27 + 2 or −25
x + 4 = −27 + 4 or −23
So, the consecutive odd integers are −27, −25, and
−23.
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Solve each equation. Check your solution.
25. 2x = 2(x − 3)
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Check:
2-4 Solving Equations with the Variable on Each Side
29. 31. SOLUTION: SOLUTION: Check:
Check:
31. SOLUTION: 33. 6.78j − 5.2 = 4.33j + 2.15
SOLUTION: Check:
Check:
35. 3.2k − 4.3 = 12.6k + 14.5
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33. 6.78j − 5.2 = 4.33j + 2.15
SOLUTION: Page 4
2-4 Solving Equations with the Variable on Each Side
35. 3.2k − 4.3 = 12.6k + 14.5
SOLUTION: Check:
numbers.
x = −2
x + 2 = −2 + 2 or 0
So, the consecutive even integers are −2 and 0.
38. MONEY Chris has saved twice the number of
quarters that Nora saved plus 6. The number of
quarters Chris saved is also five times the difference
of the number of quarters and 3 that Nora has saved.
Write and solve an equation to find the number of
quarters they each have saved.
SOLUTION: Let q be the number of quarters Nora saved.
37. NUMBER THEORY Three times the lesser of
two consecutive even integers is 6 less than six times
the greater number. Find the integers.
SOLUTION: Let x be the first consecutive even integer and x + 2
be the next consecutive even integer.
Substitute 7 for q to find the number of quarters
Chris saved.
Substitute −2 into each expression to find the even
numbers.
x = −2
x + 2 = −2 + 2 or 0
So, the consecutive even integers are −2 and 0.
38. MONEY Chris has saved twice the number of
quarters that Nora saved plus 6. The number of
quarters Chris saved is also five times the difference
of the number of quarters and 3 that Nora has saved.
Write and solve an equation to find the number of
quarters they each have saved.
SOLUTION: Let q be the number of quarters Nora saved.
So, Nora saved 7 quarters and Chris saved 20
quarters.
39. DVD A company that replicates DVDs spends
$1500 per day in building overhead plus $0.80 per
DVD in supplies and labor. If the DVDs sell for
$1.59 per disk, how many DVDs must the company
sell each day before it makes a profit?
SOLUTION: Let d be the number of DVDs.
So, the company must sell more than 1,899 DVDs
per day to make a profit.
42. REASONING Solve 5x + 2 = ax – 1 for x. Assume
that a ≠ 0. Describe each step.
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SOLUTION: Page 5
So, the company
must
sellthe
more
than 1,899
DVDsSide
2-4 Solving
Equations
with
Variable
on Each
per day to make a profit.
The correct answer is g = 6.
b. This is correct. Check the answer. 42. REASONING Solve 5x + 2 = ax – 1 for x. Assume
that a ≠ 0. Describe each step.
SOLUTION: c. This is incorrect. To eliminate –6z on the left side
of the equals sign, 6z must be added to each side of
the equation.
45. CCSS CRITIQUE Determine whether each
solution is correct. If the solution is not correct,
describe the error and give the correct solution.
a.
The correct answer is z = 1.
b.
c.
SOLUTION: a. This is incorrect. The 2 must be distributed over
both g and 5.
The correct answer is g = 6.
b. This is correct. Check the answer. eSolutions Manual - Powered by Cognero
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