Download Section 2.4 Review for Mastery

Name ________________________________________ Date __________________ Class__________________
LESSON
2-4
Review for Mastery
Solving Equations with Variables on Both Sides
Variables must be collected on the same side of the equation before the
equation can be solved.
Solve 10x = 2x − 16.
Check:
10x = 2x − 16
−2x
−2x
10x = 2x − 16
Add −2x to both sides.
−20 =? −4 − 16
8x = −16
−16
8x
=
8
8
10(−2) =? 2(−2) − 16
Divide both sides by 8.
−20 =? −20 9
x = −2
Solve 3x = 5(x + 2).
Check:
3x = 5x + 10
Distribute.
3x = 5(x + 2)
−5x −5x
Add –5x to both sides.
−15 =? 5(−3)
−2x = 10
−2x 10
=
−2
−2
3(−5) =? 5(−5 + 2)
Divide both sides by −2.
−15 =? −15 9
x = −5
Write the first step you would take to solve each equation.
1. 3x + 2 = 7x
2. −4x − 6 = −10x
3. 15x + 7 = −3x
Solve each equation. Check your answers.
4. 4x + 2 = 5(x + 10)
________________________
5. −10 + y + 3 = 4y − 13
_________________________
6. 3(t + 7) + 2 = 6t − 2 + 2t
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
2-30
Holt McDougal Algebra 1
Name _______________________________________ Date __________________ Class__________________
LESSON
2-4
Review for Mastery
Solving Equations with Variables on Both Sides continued
Some equations have infinitely many solutions. These equations are true for all values of the
variable. Some equations have no solutions. There is no value of the variable that will make
the equation true.
Solve 3x + 9 = 4x + 9 7x.
Check any value of x:
3x + 9 = 3x + 9
Combine like terms.
3x
Add 3x to each side.
+3x
9=9
True statement.
Try x = 4.
3x + 9 = 4x + 9 7x
3(4) + 9 =? 4(4) + 9 7(4)
12 + 9 =? 16 + 9 28
The solution is the set of all real numbers.
3 =? 3 Solve 2x + 6 + 3x = 5x 10.
Check any value of x:
2x + 6 + 3x = 5x 10
5x + 6 = 5x 10
5x
5x
6 = 10 Try x = 1.
Combine like terms.
Add 5x to each side.
False statement.
2x + 6 + 3x = 5x 10
2(1) + 6 + 3(1) =? 5(1) 10
2 + 6 + 3 =? 5 10
11 =? 5 There is no solution.
Solve each equation.
7. x + 2 = x + 4
________________________
10. 5x 1 4x = x + 7
________________________
8. 2x + 8 = 2x + 4
_______________________
11. 2(f + 3) + 4f = 6 + 6f
_______________________
9. 5 + 3g = 3g + 5
________________________
12. 3x + 7 2x = 4x + 10
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
2-31
Holt McDougal Algebra 1
Problem Solving
Practice C
1. x = 2
2. a = 3
3. c = −1
4. y = −3
5. d = −
11
2
7. m = 9
9. no solution
11. 6 shirts, $61
1.
3.
5.
7.
6. t = −2
1. Look for an opportunity to use the
Distributive Property.
2. Combine any like terms.
3. Collect the variable terms on one side of
the equal sign.
4. p = −6
5. x = 1
6. t = −2
10. all real numbers
12. 5 weeks, $85
Review for Mastery
1. Possible answers: add −3x to each side,
add −7x to each side
2. Possible answers: add 4x to each side,
add 10x to each side
LESSON 2–5
3. Possible answers: add 3x to each side,
add −15x to each side
5. 2
6. 5
7. no solution
8. 1
9. all real numbers
10. no solution
Practice A
1. C = K − 273
3. y =
11. all real numbers
12. −1
1
3. x = 7
2
2. x = −4
4. x = −2
4. s = r − 4t
6. j =
7. w =
v
9
8. a = bc − 3
d
r
b. 3
6−k
h
10. a. F = 2 + E − V
b. 12
Practice B
6. 9x + 18 = 0 or −9x + (−18) = 0
7. 5x + 27 = 0 or −5x + (−27) = 0
8. 3x + (−21) = 0 or −3x + 21 = 0
b
9. a. x = −
a
b. After writing the equation in the form
ax + b = 0, substitute the values of a
and b into the formula found in part a.
2
12. x = −5
5
1
T
p + 7n
3
9. a. t =
5. 2x + (−6) = 0 or −2x + 6 = 0
10. x = 3
x
5
2. f =
5. m =
Challenge
7
1. x = −
3
2. 7 days
4. 20 months
6. G
Reading Strategies
8. all real numbers
4. −48
28 feet
16 hours
B
C
11. x = −2
C
2π
2. m =
3. c =
d
4
4. n = 8 + 6m
5. p =
q − 5r
2
6. x =
−10 − z
y
7. b =
a
c
8. j =
h−4
k
9. a. p =
13. x = 7
b. 17
14. a. infinitely many solutions
y −b
x
1. r =
c − 215
5
10. a. b =
2A
h
b. 32 mm
b. no solution
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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Holt McDougal Algebra 1