Download The Addition Property of Equality Skill Builder 2.1

Skill Builder 2.1
The Addition Property of Equality
Solve each algebra equation. Complete the puzzle at the bottom to see if your work is correct.
1. 7x - 6 = 6x – 1
2. 4.5 + x = 4.5
3. x +
7 13
=
2 2
4. 3.5 = x + 2
5. 7(x + 4) = 6x + 24
6. x – 1 = −
1
2
O
10
A
5
B
-4
I
2
E
1.5
S
-10
N
0.6
L
0
R
1
2
U
11
F
6
G
3
K
9
7. 2x = x + 5
8. 2(x-1) = x
9. x + 20 = 10
10. 18 = x + 12
11. 4(x – 2) = 3(x + 1)
12. x + 11.4 = 12
1
2
3
4
5
6
7
8
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9
10
11
12
Skill Builder 2.2
The Multiplication Property of Equality
Circle the equations in each row that have the same solutions.
1. a. 2x = 8
b. x = –2x
c. –6x = –24
2. a. x = –3
b. –4x = 12
c.
b. 4(x + 2) = 16
c. x = 18
3. a.
2
x = 12
3
1
1
x=–
6
2
d. 3x + 8 = 2x + 12
d. 3x = 6x + 3
d. x = 8
4. a. 6(x – 3) = 5x – 8
b. 4(x +2) = 16
c. 15 – x = 25
d. 3x +7 = 5x – 13
5. a. 3x + 10 = 4x + 5
b. –12x = –60
c. x = 5
d. –x = –5
Solve each equation. Show your steps.
6.
x
= –2
6
7. 25 + x = 5x + 1
8. 6x + 3 = 7x
9. 2y – 8 = 2(y + 3)
10. (a – 3) = 3(a +5)
11. –18– 3(x – 4) = –3x – 6
12. 5y = 6y – 4
13. a + 10 = 2a – 4
14.
3
x=6
4
15. 9(2 – y) + 5 = 4y – 16
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Skill Builder 2.3
Solving Linear Equations
Solve each equation. Place the correct answer in the blank beside each equation.
______1. 2(x – 2) = 5(x +1)
9
b. 3
a.
7
c. −
7
3
d. –3
______2. 6x + 2x – x = 10 + 4
14
9
c.
7
4
d. 2
a. –2
b.
x
−2=8
3
a. 30
b. 10
c. –10
d. 18
______4. 2(x + 4) = 2x – 8
a. no solution
b. 4
c. all real numbers
d. –4
b. 3
c. –3
d. 6
c. 2
d. no solution
c. 0
d. all real numbers
c. no solution
d. all real numbers
______3.
x 5 3x 1
− =
−
2 3 4 6
a. –6
______5.
______6. 2(6x – 4) = -2
1
a.
2
b. −
1
2
______7. 2x + 4 = x + 4
a. 8
______8. 2x + 4x – 6x = 8
a. 0
b.
8
3
b. 8
______9. 3(4x + 5) = -33
a. 4
b.
1
4
7
3
d. –4
c. –8
d. –3
c.
______10. 4x – (2x + 5) = 11
a. 8
b. 3
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Skill Builder 2.4
Formulas and Percents
Solve each formula for m.
1.
y = mx + b
2.
am + p = t
3.
p+m–h=v
Solve each formula for A.
4.
2A
=h
b
5.
A
=l
w
6.
3b – AW = P
7.
Fill in the table.
Decimal
0.45
Fraction
45
100
a.
45%
23%
2
b.
c.
3
100
0.08
27
10
d.
8.
Percent
Fill in the table.
a.
b.
c.
Original Amount
New Amount
$1200
$885
$2500
$2100
$45
$36
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Decrease
% Decrease
Skill Builder 2.5
An Introduction to Problem Solving
Match the following mathematical expressions/equations to the English phrase/statement. Read
carefully.
______1.
A number decreased by five.
______2.
The quotient of five and a number is four.
______3.
Three more than twice a number is five.
______4.
Eight less than a number.
______5.
A number increased by two is three times the number.
______6.
Twice the difference of a number and four is six.
______7.
Eleven is the same as a number less four.
______8.
Three times a number increased by 4 is seven.
______9.
Two less than six times a number is five.
______10.
The difference of a number and four is ten.
______11.
Nine more than the product of eight and a number .
a.
c.
e.
g.
2x + 3 = 5
x–8
11 = x – 4
8x + 9
b.
d.
f.
h.
i.
x+3=5
j.
k.
m.
o.
3x = 7 + 4
5–x
x÷5=4
8
+9
x
6x – 2 = 5
x = 10 – 4
l.
n.
p.
2x – 4 = 6
3x + 4 = 7
x–5
2 – 6x = 5
5
=4
x
x + 2 = 3x
11 = 4 – x
x – 4 = 10
r.
8–x
t.
2(x – 4) = 6
q.
s.
u.
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Skill Builder 2.6
Solving Linear Inequalities
Fill in the table.
Equation
1.
Graph
x ≥ –4
{x | x < 2}
2.
3.
x≥3
4.
5.
1
}
2
{x | x ≤
5
}
3
6x < 4 + 6x
{x | x < 0}
8.
9.
{x | x >
x<4
6.
7.
Set Builder
Notation
2x ≥ 2x + 6
{x | x > –3.5}
10.
Fill in the blank:
When multiplying or dividing both sides of an inequality by a negative number,
_______________ the inequality symbol.
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