Beginning Algebra Must Be APA Format All Problems Must Have
Beginning Algebramust Be Apa Formatall Problems Must Have Work Shownmu
Beginning Algebra must be APA format all problems must have work shown must be done by 12pm EST. on 2/15/. Is 12 a solution to the equation 7 – x = 5? 2. Is –9 a solution to the equation 9 – 8x = 81? 3. Solve -2x+7>=. Solve 3(x-5) 10x – . An arithmetic student needs an average of 70 or more to receive credit for the course. She scored 76, 69, and 84 on the first three exams. Write a simplified inequality representing the score she must get on the last test to receive credit for the course. 26. The length of a rectangle is 2 in. more than twice its width. If the perimeter of the rectangle is 28 in., find the width of the rectangle. 27. Solve and check: 6x=4(x-. Solve 1/4x23.5
Paper For Above instruction
Beginning Algebra must adhere to APA format, with all problems demonstrating work and clear solutions. The assignment is due by 12:00 pm EST on February 15. The problem set covers fundamental algebraic concepts, including solving equations, inequalities, word problems, and geometric applications. The following paper provides detailed solutions to each problem, illustrating the step-by-step processes involved, as well as interpretations and checks where applicable. This comprehensive approach ensures understanding of each concept and skill necessary in beginning algebra.
1. Is 12 a solution to the equation 7 – x = 5?
To verify if x = 12 satisfies the equation 7 – x = 5, substitute x = 12:
7 – 12 = 5
-5 ≠ 5
Since the left side equals -5 and the right side is 5, x = 12 is not a solution.
2. Is –9 a solution to the equation 9 – 8x = 81?
Substitute x = –9 into the equation:
9 – 8*(–9) = 81
9 + 72 = 81
81 = 81
Yes, x = –9 is a solution to the equation.
3. Solve -2x + 7 ≥
Given that the inequality is incomplete, assume it is:
-2x + 7 ≥ 0
Subtract 7 from both sides:
-2x ≥ -7
Divide both sides by -2 (remember, dividing by a negative reverses the inequality):
x ≤ 3.5
Thus, the solution set is all x less than or equal to 3.5.
4. Solve 3(x - 5)
Distribute:
3x - 15
Subtract 3x from both sides:
-15
Add 2 to both sides:
-13
Therefore, x > -13.
5. Solve 8x + 2 = 7x
Subtract 7x from both sides:
8x - 7x + 2 = 0
x + 2 = 0
Subtract 2:
x = -2
6. Solve 7x – 0.96 = 6(x – 0)
Distribute:
7x - 0.96 = 6x
Subtract 6x from both sides:
x - 0.96 = 0
Add 0.96 to both sides:
x = 0.96
7. Solve for x: 4x = –
Given incomplete inequality, assuming it is:
4x = -k (where k is a positive number). Since no numerical value is provided, cannot solve further.
8. A company estimates that 5% of the parts are defective. If 8 defective parts are found, find the total manufactured that week.
Let N be the total number of parts manufactured:
0.05N = 8
Divide both sides by 0.05:
N = 8 / 0.05
N = 160
Therefore, 160 parts were manufactured.
9. Solve for x: 35 – 7x = .
Incomplete; assuming the equation is:
35 – 7x = 0
Subtract 35:
-7x = -35
Divide:
x = 5
10. Solve for x: – 5 = .
Incomplete; assuming:
–5x = some value. Cannot proceed without full equation.
11. Solve 4(x – 2) + 4x = 5x +
Incomplete; assuming:
4(x – 2) + 4x = 5x
Distribute:
4x – 8 + 4x = 5x
Combine like terms:
8x – 8 = 5x
Subtract 5x:
3x – 8 = 0
Add 8:
3x = 8
Divide:
x = 8/3 ≈ 2.67
12. Solve 7x – 3 + 3x = 10x –
Assuming:
7x – 3 + 3x = 10x
Combine:
10x – 3 = 10x
Subtract 10x:
-3 = 0
No solution; inconsistent.
13. Solve –10x + 1 – 7x = –17x +
Assuming:
-10x + 1 – 7x = -17x
Combine:
-17x + 1 = -17x
Subtract -17x from both sides:
1 = 0
No solution; inconsistent.
14. Solve the literal equation for y: x + 5y =
Incomplete; assuming:
x + 5y = c (constant)
Solve for y:
5y = c – x
y = (c – x)/5
15. A rectangular solid with length 5cm, width 2cm, volume 100cm³. Find height.
Volume V = L × W × H
100 = 5 × 2 × H
100 = 10H
H = 10cm
16. Translate to algebraic equation: 1 less than 15 times a number is 9 times the same number.
Let x be the number:
15x – 1 = 9x
Subtract 9x:
6x – 1 = 0
6x = 1
x = 1/6
17. Sum of three consecutive odd integers is 201. Find the integers.
Let the smallest be x, then the others are x + 2 and x + 4:
x + (x + 2) + (x + 4) = 201
3x + 6 = 201
3x = 195
x = 65
The integers are 65, 67, and 69.
18. Truck catch-up problem.
First truck distance after 2 hours:
Distance = 35 mi/hr × 2 hr = 70 miles
Let t be the time after 9:00 a.m. when second truck catches up:
Second truck starts at 9:00 + 2 hours = 11:00 a.m.
Second truck's distance after t hours:
70t miles + 70 miles per hour × t = distance of first truck:
35 × (t + 2) = 70t
Solve:
35t + 70 = 70t
70 = 70t - 35t
70 = 35t
t = 2 hours
Catch-up occurs at 11:00 a.m. + 2 hours = 1:00 p.m.
19. Isosceles triangle side lengths.
Let each equal side be x, and the base be x – 1:
Perimeter: 2x + (x – 1) = 20
3x – 1 = 20
3x = 21
x = 7
Sides: 7 in., 7 in., base 6 in.
20. Find the amount in "318 is 53% of 600".
Calculate:
0.53 × 600 = 318
Amount is 318.
21. Monthly interest rate on balance.
Interest charged: $126 on $1800
Monthly rate = (Interest / Principal) × 100:
(126 / 1800) × 100 ≈ 7%
22. Markup problem.
Marked-up price = original cost + $150
Markup is 50% of original cost:
150 = 0.50 × original cost
Original cost = 150 / 0.50 = $300
23. Solve solution set inequality: 8x + 3
Assuming:
8x + 3
Subtract 4x:
4x + 3
4x
x
24. Solve 5x + 12 > 10x –
Assuming:
5x + 12 > 10x
Subtract 5x:
12 > 5x
x
25. Inequality for last test score.
Average ≥ 70:
(76 + 69 + 84 + x) / 4 ≥ 70
(229 + x) / 4 ≥ 70
229 + x ≥ 280
x ≥ 51
She needs at least 51 on the last test.
26. Rectangle dimensions.
Let width = w:
Length = 2w + 2
Perimeter:
2(length + width) = 28
2(2w + 2 + w) = 28
2(3w + 2) = 28
6w + 4 = 28
6w = 24
w = 4 inches
27. Solve and check: 6x=4(x-.
Assuming:
6x = 4x – c (Incomplete), but if the intended is 6x = 4x:
Subtract 4x:
2x = 0
x = 0
Check:
6(0) = 0 and 4(0) = 0
Valid solution.
28. Solve 1/4x ≤ 3/.
Assuming:
(1/4) x ≤ 3
Multiply both sides by 4:
x ≤ 12
29. Solve 8x – 7 ≤ 7x –.
Assuming:
8x – 7 ≤ 7x
Subtract 7x:
x – 7 ≤ 0
x ≤ 7
30. Solve -5x > 23.5
Divide both sides by -5 (reverse inequality):
x
References
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