Download 17 Practice Set 2.1 The Addition Property of Equality Identi

Name _________________________________
Date _______________________
Practice Set 2.1
The Addition Property of Equality
Identify each equation as linear or not linear.
1.
x + 7 = 15
1. _______________
2.
x2 − 3 = 9
2. _______________
3.
11
=4
x
3. _______________
4.
5.
5 x + π = 0.3
4. _______________
x +1 = 7
5. _______________
Solve each equation using the addition property of equality. Be sure to check your proposed
solutions.
6.
x − 9 = −11
6. _______________
7.
−6 = x+9
7. _______________
8.
− 8 + x = −8
8. _______________
9.
18 = x + 12
9. _______________
10.
x + 20 = 10
10. ______________
17
Name _________________________________
Date _______________________
11.
4.5 + x = 4.5
11. ______________
12.
x + 11.4 = 12
12. ______________
13.
x–1= −
1
2
13. ______________
14.
3.5 = x + 2
14. ______________
15.
x+
7 13
=
2 2
15. ______________
16.
2x = x + 5
16. ______________
17.
7x – 6 = 6x – 1
17. ______________
18.
2(x – 1) = x
18. ______________
19.
7(x + 4) = 6x + 24
19. ______________
20.
4(x – 2) = 3(x + 1)
20. ______________
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Name _________________________________
Date _______________________
Practice Set 2.2
The Multiplication Property of Equality
Solve each equation using the multiplication property of equality. Be sure to check your
proposed solution.
1.
x
= −2
6
1. _______________
2.
–4x = 12
2. _______________
3.
2
x = 12
3
3. _______________
4.
–12x = –60
4. _______________
5.
–x = –5
5. _______________
6.
3
x=6
4
6. _______________
7.
− 10 x = 5
7. _______________
8.
4x = 0
8. _______________
9.
5
25 = − x
7
9. _______________
10.
−8 =
1
x
2
10. _______________
19
Name _________________________________
Date _______________________
Solve each equation using both the addition and multiplication properties of equality. Be sure to
check your proposed solutions.
11.
25 + x = 5x + 1
11. _______________
12.
4 x + 8 = 16
12. _______________
13.
3x +7 = 5x – 13
13. _______________
14.
a − 3 = 3a + 15
14. _______________
15.
a + 10 = 3a – 4
15. _______________
16.
−x−4= 4
16. _______________
17.
5x + 1 = 2 x − 5
17. _______________
18.
2 z + 7 = 8z + 1
18. _______________
19.
6x − 4 = 4x + 7
19. _______________
20.
x + 9 = 3 x + 15
20. _______________
20
Name _________________________________
Date _______________________
Practice Set 2.3
Solving Linear Equations
Solve each equation. Be sure to check your proposed solution by substituting it for the variable
in the original equation.
1.
2(x – 2) = 5(x +1)
1. _______________
2.
6x + 2x – x = 10 + 4
2. _______________
3.
3( x + 4) = 5( x − 2)
3. _______________
4.
2(6x – 4) = –2
4. _______________
5.
2x + 4 = x + 4
5. _______________
6.
3 x + 2 x − 8 x = −27
6. _______________
7.
3(4x + 5) = –33
7. _______________
8.
4x – (2x + 5) = 11
8. _______________
9.
2( x + 4) − 5 x = 4( x − 5)
9. _______________
10.
5( x − 3) = 3(2 x − 4)
10. _______________
11.
7 x − (2 x + 4) = 3( x − 6)
11. _______________
12.
− 9( x + 3) = 4 x − ( x + 3)
12. _______________
21
Name _________________________________
Date _______________________
13.
2(3x + 1) = 2(5 x − 1)
13. _______________
14.
− 18 − 3( x − 4) = −2 x − 6
14. _______________
15.
9(2 − y ) + 5 = 4 y − 16
15. _______________
Solve and check each equation. Begin your work by rewriting each equation without fractions.
16.
x
−2=8
3
16. _______________
17.
x 5 3x 1
− =
−
2 3 4 6
17. _______________
18.
x−2
x+4
+1 =
4
3
18. _______________
Solve each equation. Use words or set notation to identify equations that have no solution or
equations that are true for all real numbers.
19.
2( x + 4) = 2 x − 8
19. _______________
20.
2 x + 4 x − 5 x + 11 = x + 13 − 2
20. _______________
22
Name _________________________________
Date ______________________
Practice Set 2.4
Formulas and Percents
Solve each formula for the specified variable.
1.
P = a + b + c for a
1. _______________
2.
V = lwh for l
2. _______________
3.
y = mx + b for x
3. _______________
4.
A
= l for w
w
4. _______________
5.
2A
= h for A
b
5. _______________
6.
A=
7.
PV = nRT for R
7. _______________
8.
Ax + By = C for B
8. _______________
1
h(a + b) for h
2
6. _______________
Express each percent as a decimal.
9.
15%
9. _______________
10.
9.25%
10. _______________
11.
3
%
4
11. _______________
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Name _________________________________
Date ______________________
Express each decimal as a percent.
12.
0.71
12. _______________
13.
0.015
13. _______________
14.
49
14. _______________
Use the percent formula, A = PB; A is P percent of B to solve exercises 15-20.
15.
What is 7% of 100?
15. _______________
16.
8 is 40% of what?
16. _______________
17.
16% of what number is 40?
17. _______________
18.
18 is what percent of 72?
18. _______________
19.
What percent of 7.5 is 1.125?
19. _______________
20.
If 45 is decreased to 36, the decrease is what percent
of the original number?
20. _______________
24
Name _________________________________
Date _______________________
Practice Set 2.5
An Introduction to Problem Solving
Let x represent the number. Use the given conditions to (a) write an equation and then (b) solve
the equation to find the number.
1.
A number decreased by five is eleven.
1a. _______________
b. _______________
2.
The quotient of five and a number is negative five.
2a. _______________
b. _______________
3.
Three more than twice a number is five.
3a. _______________
b. _______________
4.
Eight less than a number is eighteen.
4a. _______________
b. _______________
5.
A number increased by two is three times the number.
5a. _______________
b. _______________
6.
Twice the difference of a number and four is six.
6a. _______________
b. _______________
7.
Eleven is the same as a number less four.
7a. _______________
b. _______________
8.
Three times a number increased by four is negative eight.
8a. _______________
b. _______________
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Name _________________________________
9.
Date _______________________
Two less than six times a number is sixteen.
9a. _______________
b. _______________
10.
The difference of a number and four is ten.
10a. ______________
b. ______________
11.
Nine more than the product of eight and a number is one.
11a. ______________
b. ______________
12.
Three times the sum of a number and five is
negative twenty-one.
12a. ______________
b. ______________
13.
Six more than two times a number is that number
less eleven.
13a. ______________
b. ______________
14.
If the quotient of twice a number and three is decreased
by four, the result is negative ten.
14a. ______________
b. ______________
15.
Four times a number less eight is the same as twice a
number increased by four.
15a. ______________
b. ______________
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Name _________________________________
Date ______________________
Practice Set 2.6
Problem Solving in Geometry
Use the formulas for perimeter, area, circumference and volume to solve the problems.
1.
Find the area of a rectangle with a length of 16 inches and a
width of 7 inches.
1. _______________
2.
Find the perimeter of a rectangle with a length of 24 centimeters
and a width of 10 centimeters.
2. _______________
3.
Find the area of a triangle that has a base 10 inches and a
height of 5 inches.
3. _______________
4.
Find the length of a rectangle in which the width is 8 meters
and the area is 116 m2.
4. _______________
5.
Find the area of a circle that has a radius of 3 inches. Express
your answer in terms of π, then round to the nearest whole
number.
5. _______________
6.
Find the area of a circle with a diameter of 14 millimeters.
Express your answer in terms of π, then round to the nearest
whole number.
6. _______________
7.
Find the circumference of a circle with a radius of 5
centimeters. Express your answer in terms of π, then round to
the nearest whole number.
7. _______________
8.
Find the circumference of a circle with a diameter of
8 decimeters. Express your answer in terms of π, then
round to the nearest whole number.
8. _______________
9.
Find the radius of a circle that has a circumference of 18π feet.
9. _______________
10.
Find the diameter of a circle that has an area of 49π yd2.
10. _______________
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Name _________________________________
Date ______________________
11.
Find the volume of a cube with a length of 2.5 inches.
11. _______________
12.
Find the volume of a rectangular solid with a length of
7 inches, a width of 5.5 inches and a height of 3 inches.
12. _______________
13.
Find the volume of a circular cylinder with a height of
3 feet and a radius of 1.5 feet. Express your answer in terms
of π, then round to the nearest whole number.
13. _______________
14.
Find the volume of a ball if the diameter is 12 inches. Express
your answer in terms of π then round to the nearest whole
number.
14. _______________
15.
The largest angle of a triangle is six more than three times the
smallest angle. The third angle is twice the smallest. Find the
measure of each angle.
15. _______________
16.
One angle of a triangle is twice the first angle. The third angle
is eight more than the first angle. Find the measure of each
angle.
16. _______________
17.
Two angles are complementary. One measures 73°. What is
the measure of the other angle?
17. _______________
18.
Two angles are supplementary. One angle is 42°. Find the
measure of its supplement.
18. _______________
19.
Two angles are supplementary. One angle measures x and the
other 3x + 4. Find the measure of each angle.
19. _______________
20.
Two angles are complementary. One angle measures x and
the other 2x + 3. Find the measure of each angle.
20. _______________
28
Name __________________________________
Date _______________________
Practice Set 2.7
Solving Linear Inequalities
(a) Graph the solutions of each inequality on a number line and then (b) express the solution set
of each inequality in interval notation.
1.
x ≥ −4
1a.
b. _____________________
2.
x<2
2a.
b. _____________________
3.
x>3
3a.
b. _____________________
4.
x≤
1
2
4a.
b. _____________________
5.
–2 < x ≤ 4
5a.
b. _____________________
6.
0≤x≤3
6a.
b. _____________________
Use the addition property of inequality to solve each inequality. (a) Graph the solutions of each
inequality on a number line and then (b) express the solution set of each inequality in interval
notation.
7.
x+4>7
7a.
b. _____________________
29
Name __________________________________
8.
x–3≤2
Date _______________________
8a.
b. _____________________
9.
4x + 9 > 3x + 4
9a.
b. _____________________
10.
x+
1 1
<
2 8
10a.
b. ____________________
11.
4x + 2 ≥ 3 + 3x
11a.
b. ____________________
Use the multiplication property of inequality to solve each inequality. (a) Graph the solutions of
each inequality on a number line and then (b) express the solution set of each inequality in
interval notation.
12.
1
x > −2
2
12a.
b. ____________________
13.
x
≤1
4
13a.
b. ____________________
14.
3x ≥ 9
14a.
b. ____________________
15.
–4x < –12
15a.
b. ____________________
16.
–x ≥ 3
16a.
b. ____________________
30
Name __________________________________
Date _______________________
Use both the addition and multiplication properties of inequality to solve each inequality.
(a) Graph the solutions of each inequality on a number line and then (b) express the solution set
of each inequality in interval notation.
17.
–(x + 6) > –5
17a.
b. ____________________
18.
2(4x + 1) ≤ –6
18a
b. ____________________
19.
4x + 9 > 2x + 3
19a.
b. ____________________
20.
6(x – 4) ≥ 3(x – 5)
20a.
b. ____________________
Solve each inequality.
21.
6x < 4 + 6x
21. ____________________
22.
2x ≥ 2x + 6
22. ____________________
31
Name __________________________________
32
Date _______________________