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Review for MA098
Equations & Inequalities
Solve for the indicated variable.
1) V = 1Bh for h 1)
3
Answer Yes or No.
2) Is 12 a solution to x - 5 = 1x + 1? 2)
2
Translate the graph to an inequality using the variable x.
3) 3)
Find the value of the variable that satisfies the equation.
4) 21 1x 2x 4)
- =
Translate the English statement into an inequality.
5) The speed of the bike is more than 7 mph. (Use the variable s for the speed.) 5)
Solve the problem using a known formula.
6) A contestant in a 25-mile race finished in 7 hours. What was her average rate during the 6)
race? (Round to the nearest tenth, if necessary.)
Provide an appropriate response.
Solve for b. A 1h(a b)
7) = 2 + 7)
Solve for the variable.
8) 3(x 6) 4(x 7) 8)
+ = -
Solve for x. Be sure to reduce your answer. Check your solution.
9) -5x = -30 9)
Find the value of the variable that satisfies the equation.
10) 6x + 4 = -2 + 2x 10)
Solve.
1(x 6) 1(x 8)
11) 5 + = 6 + 11)
Solve the inequality.
12) 12x 14 2(5x 16) 12)
- K -
1
Solve for the indicated variable.
P S S S for S
13) = 1+ 2+ 3 3 13)
Answer Yes or No.
Is 1 a solution to 1 (x 6) 1x 8?
14) 5 + = 7 + 7 14)
Solve for the variable.
15) 2(2x 3) 3(x 5) 15)
- = +
Solve the inequality. Graph the results.
16) 9 - 2x - 11L -3x + 8 16)
Provide an appropriate response.
17) Solve the formula A = LW for L. Use the result to find the room's length if the width of a 17)
room is 6 feet, and the area of the room is 84 square feet.
Find the value of the variable that satisfies the equation.
18) 1x - 1 = -4 18)
5 5
19) -7x + x = -54 19)
Translate the English statement into an inequality.
20) The rocket must reach a speed of at least 942 mph. (Use the variable V for speed.) 20)
Solve the inequality.
21) 0.1(1.1 x) 1.8 3.7(x 0.3) (Round to two decimal places if necessary) 21)
- + > -
Solve for x. Check your answers.
22) x 15 5 22)
- =
Answer Yes or No.
Is 1 a solution to 1(x 6) 1x 8?
23) - 5 + = 7 + 7 23)
Solve the inequality. Graph the results.
x 6 13
24) + < 24)
Find the value of the variable that satisfies the equation.
25) 14 8x 6 25)
- = -
2
Solve for x. Be sure to reduce your answer. Check your solution.
26) -x = -12 26)
Solve the inequality. Graph the results.
27) 5x + 3 K 4x - 9 27)
Solve for x. Check your answers.
28) 10 15 x 2 28)
- = +
Find the value of the variable that satisfies the equation.
29) 1x - 5 = 1 29)
7
Solve.
30) 4(x 5) 4x 20 30)
+ = +
Solve for the variable.
31) 4(y 3) 5(y 5) 31)
+ = -
Determine if the given solution is correct. If it is not, find the solution.
32) Is 3 the solution to x 4 6 5? 32)
- + = -
Solve.
33) 12(x 2) 6(2x 2) 12 33)
- = - -
Find the value of x that satisfies the equation.
x 1 5
34) - 6 = 12 34)
35) 7.5 x 22 35)
+ =
Solve.
The formula for the volume of a cone is V 1Bh. If the Volume, V, is 36 cubic centimeters
36) = 3 36)
and the height, h, is 9 centimeters, find the base, B, of this cone.
Replace the ? by < or >.
37) -3 ? - 6 37)
Find the value of x that satisfies the equation.
x 1 1
38) + 5 = 2 38)
3
Solve.
39) 0.1(50) 0.7x 0.3(50 x) 39)
- + = +
Find the value of the variable that satisfies the equation.
40) 9x + 4 = 76 40)
Solve for the variable.
41) 5(x 8) 6(x 5) 41)
+ = -
Solve for x. Check your answers.
42) x 1 13 42)
- =
Find the value of the variable that satisfies the equation.
43) -8x + 6 = -2 - 2x 43)
Solve for the indicated variable.
2
S 2Δrh 2Δr for h
44) = + 44)
Solve for x. Be sure to reduce your answer. Check your solution.
45) - 1 x = 0 45)
19
Solve for x. Check your answers.
46) 2 12 9 6 x 10 46)
- + = + -
Solve.
47) 2x - 1x =4 47)
5 3
The formula for the perimeter of a rectangle is P 2L 2W. If the length, L, is 2 meters and
48) = + 48)
the width, W, is 3 meters find the perimeter, P, of this rectangle.
Find the value of x that satisfies the equation.
1 1 x 1
49) 3 - 2 = - 4 49)
Graph the inequality on the number line.
x 4
50) L- 50)
4
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