Inequalities Quiz Study Guide
Name________________________
Date_____________Block_______
Solve each inequality. ​ ANSWERS IN BLUE
1) 3(− 9x + 4) − 28 > 38 distribute
− 27x + 12 − 28 > 38 CLT
− 27x − 16 > 38 add 16
− 27x > 54 divide by -27 FLIP
x < −2
2)
3x+15
4
7) 6 ≥ 37 x − 1
+1
+1
7
7 ≥ 3x
3 * 7 ≥ 37 x * 3 OR​ 73 * 7 ≥ 37 x *
21 ≥ 7x
21
7x
7 ≥ 7 answer 3 ≥ x or x ≤ 3
3
7
+ 18 ≤ 22
-18 -18
3x+15
4 ≤4
4 * 3x+15
4 ≤
8) 6x − 2x + 8 > 36 CLT
4x + 8 > 36 sub 8
4*4
3x + 15 ≤ 16
-15
-15
3x ≤ 1 then
3x
3
≤
1
3
ans x ≤
1
3
3) 4x − 1(9x + 25) < 100 distribute
4x − 9x − 25 < 100 CLT
− 5x − 25 < 100 add 25
− 5x < 125 divide by -5 FLIP
x > − 25
4) 2x + 10 ≥ 7(x + 1)
x ≤−
3
5
4x >28 divide by 4
​ X>7
9) 2(x − 3) + 12(− 3x + 18) < 278
2x − 6 − 36x + 216 < 278
− 34x + 210 < 278
− 34x + 210 < 278
-210
-210
− 34x < 68
−34x
68
−34 < −34 flip x >− 2
5) 7 − 3x ≤ 16
x ≥− 3
6) − 2(x + 3) < 4x − 7
10) 19 ≥ 65 x + 11
48
48
5 ≥ x or x ≤ 5
− 2x − 6 < 4x − 7 then add 6
− 2x < 4x − 1 subtract 4x
− 6x < − 1 divide by -6 and FLIP
x > 61
Write the inequality problem and solve for each word problem
11) Four more than twice a number x is less than three times the sum of the number x and five
2x +4 <3(x + 5) distribute to get 2x +4 < 3x +15 subtract 4 to get 2x < 3x +11 subtract 3x so we get
-1x < 11, divide by negative and flip the inequality​ ​x>-11
12) An Amusement park charges a $10 entrance fee. Each ride costs $1.75. If your mom gave you $35 to
spend at the park, what is ​the most​ number of rides you can go on?
25
10 + 1.75x ≤ 35 subtract 10 1.75x ≤ 25 then divide by 1.75 1.75x
1.75 ≤
1.75 ans x ≤ 14.28 round
down because this is less than, your answer is​ x ≤ 14 14 rides is the most you can ride.
Inequalities Quiz Study Guide
Name________________________
Date_____________Block_______
13) Mike wants to buy his mom a new watch for her birthday. The watch he has found costs $65. Mike has
$13.50 from previous chores and will make $4.25 for each car he washes. Mike must wash ​at least
how many cars to afford the watch? 13.50 + 4.25x ≥ 65 subtract 13.50
4.25x ≥ 51.50 divide by 4.25
4.25x
51.50
4.25 ≥ 4.25 answer x ≥ 12.1176 round up so​ x ≥ 13 Mike needs to wash
at least 13 cars.
14) The perimeter of a rectangle must be ​at least​ 50 inches. If the length is 5 more than triple the width,
what are the minimum dimensions for the rectangle? ​(Remember: 2L + 2W=P)
2L + 2W ≥ 50 L= 3w+5 plug it in 2(3W + 5) + 2W ≥ 50 distribute 6W + 10 + 2W ≥ 50 CLT
8W + 10 ≥ 50 subtract 10 8W ≥ 40 , then divide by 8​ W ≥ 5 Find the length 3(5) +5, L ≥ 20
15) Deleted because it was missing information.