Module 03 Exercise by Cherise Weiss
Each problem is worth 5 points for a total of 50 points. Please enter your
answers and calculations on the second page using the Equation Editor.
1. Solve for x using the addition principle: −8 + 𝑥 = −24
1
3
2. Solve for y using the addition principle: = − 8 + 𝑦 = − 4
𝑦
3. Solve for y using the multiplication principle: = −6
5
4. Solve for a using the addition and multiplication principles: 14 − 6𝑎 = −2𝑎 + 3
5. Solve for t. Clear fractions first:
2
𝑡+4=
3
1
6
𝑡
6. Solve for x: 𝑦 = 𝑏𝑥 − 𝑐
7. Selena left a 15% tip for a meal. The tip was $8.40. What was the cost of the meal before
the tip?
8. Jake paid $100.70, for a color printer. This cost included a 6% tax. How much did the
printer itself, before the tax, cost?
9. Solve this inequality for x using the addition principle: 2𝑥 + 4 > 𝑥 + 7
10. Solve for y using the addition and multiplication principles: 18 − 10𝑦 ≤ 63 + 5𝑦
NAME: Cherise Weiss
Module 03 Exercise Answers
Faculty
Comments
#
Answer
1
𝑥 = −16
2
3
4
𝑦= −
5
8
𝑡 = −30
𝑎=
11
4
Calculations
− 8 + 𝑥 = −24; 8 + (−8) + 𝑥 = −24 + (−8); 𝑥 = −16
1
3 1 1
1 3
1 ∙1 3 ∙2
− +𝑦 = − ; − +𝑦 = − ; 𝑦 =
−
;𝑦
8
4 8 8
8 4
8 ∙1 4 ∙2
1 6
5
= − ; 𝑦= −
8 8
8
𝑦
1
= −6; 5 ∙ 𝑦 = 5 ∙ (−6); 1 ∙ 𝑡 = −30; 𝑡 = −30
5
5
14 − 6𝑎 = −2𝑎 + 3; 14 − 6𝑎 + (−2𝑎)
= −2𝑎 + 2𝑎 + 3; 14 − 14 − 4𝑎 = 3 − 14;
=
5
−8 = 𝑡
6
𝑦+𝑐
=𝑥
𝑏
7
$56.00
Was the
cost of
the meal
before
the tip
−11
11
;𝑎 =
−4
4
−4𝑎
−4
2
1
2
1
2
𝑡 + 4 = 𝑡; 6 ( 𝑦 + 4) = 6 ( 𝑡) ; 6 ∙ 𝑡 + 6 ∙ 4
3
6
3
6
3
1
= 6 ∙ 𝑡; 4𝑡 + 24 = 1𝑡; 4𝑡 − 4𝑡 + 24
6
24
−3𝑡
= 1𝑡 − 4𝑡;
=
; −8 = 𝑡
−3
−3
𝑦 = 𝑏𝑥 − 𝑐; 𝑦 + 𝑐 = 𝑏𝑥;
$8.40 = 15% ∙ 𝑦; 8.40 = 0.15𝑦;
𝑦+𝑐
=𝑥
𝑏
8.40
0.15
=
; 𝑦 = 56
0.15
0.15
8
$94.66
$100.70 ∙ 6%; 100.70 ∙ 0.06 = 6.04; 100.70 − 6.04 = 94.66
Was the
cost
before
taxes
9
𝑥 >3
2𝑥 + 4 > 𝑥 + 7; 2𝑥 + 4 − 4 > 𝑥 + 7 − 4; 2𝑥 > 𝑥 + 3; 2𝑥 − 𝑥
> 𝑥 + 3 − 𝑥; 𝑥 > 3
10
3 ≤𝑦
18 − 10𝑦 ≤ 63 + 5𝑦; 18 − 10𝑦 + 10𝑦 ≤ 63 + 5𝑦 + 10𝑦; 18
≤ 63 + 15𝑦; 63 − 18 ≤ 63 + 15𝑦 − 63; 45
45
15𝑦
≤ 15𝑦;
≤
; 3 ≤𝑦
15
15