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Welcome to our Basic Algebra Quiz! Whether you're a student looking to sharpen your algebraic skills or someone who simply enjoys the challenge of mathematical puzzles, this quiz is designed to test and enhance your knowledge of fundamental algebra concepts. Basic algebra is mathematics that is more abstract than arithmetic. Algebra is a cornerstone of mathematics, and it's essential for problem-solving in various fields, from science and engineering to finance and daily life. Our quiz covers a range of topics, from solving equations to working with variables, expressions, and inequalities.
Do you know the tips and tricks to solve algebra? Read moreThis basic algebra quiz will test your ability to solve basic Algebra problems. We have curated a variety of questions that will help in practicing basic algebra concepts. If you have studied it well, this algebra quiz will be perfect for you. All the best! Do not forget to share the quiz with others who wish to practice this mathematical concept. Whether you're preparing for an algebra test, brushing up on your math skills, or just enjoying the mental exercise, this quiz is an excellent resource. Are you ready to dive into the world of algebra and expand your mathematical knowledge? Let's get started!
Basic Algebra Questions and Answers
1.
7 + 2x = 15
Find x.
Explanation The correct solution for the equation 7 + 2x = 15 is x = 4.Here's how we solve it:Subtract 7 from both sides:
(7 + 2x) - 7 = 15 - 7
2x = 8Divide both sides by 2:
2x / 2 = 8 / 2
x = 4Therefore, x = 4 is the only solution to the equation.
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2.
Y = 7x + 3
Where does this line cross the y-axis?
A.
(0,3)
B.
(3,0)
C.
(1,2)
D.
(7,3)
E.
(3,7)
Correct Answer A. (0,3)
Explanation In the equation y = 7x + 3, to find where the line crosses the y-axis, you need to determine the y-coordinate when x is equal to 0. This is because the y-axis is where x = 0.
So, substitute x = 0 into the equation:
y = 7(0) + 3
y = 0 + 3
y = 3
The line crosses the y-axis at the point (0, 3).
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3.
Y = 27j - 7 - 7j.
If y = 13 what will j be equal to.
Correct Answer 1
Explanation If y = 27j - 7 - 7j, and we know that y = 13, we can substitute y with 13 in the equation. Therefore, 13 = 27j - 7 - 7j. Simplifying this equation, we get 13 = 20j - 7. Adding 7 to both sides, we have 20 = 20j. Dividing both sides by 20, we find that j = 1.
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4.
Ben Dover pays $40 per month to attend a weekly yoga class. His sister Ilene Dover gets a discount at her yoga class and pays $35 per month. Over the course of one year, how much more money does Ben pay a year to attend his yoga class?
A.
62
B.
55
C.
75
D.
60
E.
25
Correct Answer D. 60
Explanation Ben pays $40 per month for his yoga class, while his sister pays $35 per month for hers. To calculate how much more money Ben pays a year, we need to find the difference between their monthly payments and multiply it by 12 (months in a year). The difference is $40 - $35 = $5. Therefore, Ben pays $5 more per month. Multiplying this by 12, we get $5 * 12 = $60. So, Ben pays $60 more a year to attend his yoga class.
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5.
F(x) = 17x - 30
Find f(2) - f(1)
Correct Answer 17
Explanation To find f(2) - f(1), we substitute 2 and 1 into the given function f(x) = 17x - 30.
f(2) = 17(2) - 30 = 4
f(1) = 17(1) - 30 = -13
Therefore, f(2) - f(1) = 4 - (-13) = 17.
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6.
Robin Banks is driving away in her getaway car. Willie Ketchup is chasing him in his patrol car. Robin is driving 50 mph and is 100 miles away from the border. Willie is 50 miles behind Robin, and is driving 75 mph. Will Robin reach the border before Willie catches her?
A.
Yes, he will reach it 10 mins before Willie
B.
No, Willie will catch him 10 miles before the border
C.
They will reach it at the same time.
D.
No, Robin will spend 25 years in a federal prison.
E.
Yes, Robin will spend his years rich, sitting on a beach.
Correct Answer C. They will reach it at the same time.
Explanation In the thrilling chase between Robin Banks and Willie Ketchup, the outcome depends on their speeds and the distance to the border:Robin:Speed: 50 mphDistance to border: 100 milesWillie:Speed: 75 mphDistance to Robin: 50 miles (since he's 50 miles behind)Analysis:Relative Speed: Willie gains on Robin by 75 mph - 50 mph = 25 mph.Time for Robin to reach the border: Robin needs to cover 100 miles at 50 mph, so it will take him 100 miles / 50 mph = 2 hours.Time for Willie to catch Robin: Since Willie is 50 miles behind and gains 25 mph, he'll need 50 miles / 25 mph = 2 hours to catch Robin.Conclusion:Therefore, both Robin and Willie will reach the border at the same time! Although Willie can close the distance between them, he won't be able to catch Robin before they reach the border.So, the answer is They will reach it at the same time.
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7.
What is the slope of a straight line that connects the following points.(1,2) & (4,11)
Correct Answer 3
Explanation The slope of the line connecting the points (1, 2) and (4, 11) can be calculated using the formula:Slope = (y2 - y1) / (x2 - x1)where:x1 and y1 are the coordinates of the first point (1 and 2 in this case)x2 and y2 are the coordinates of the second point (4 and 11 in this case)Plugging in the values:Slope = (11 - 2) / (4 - 1)Slope = 9 / 3Slope = 3Therefore, the slope of the line connecting the points (1, 2) and (4, 11) is 3. This means that for every 3 units the line goes up vertically (y), it goes 1 unit to the right horizontally (x).
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8.
Solve for y in the equation: y – 13 = –3
A.
10
B.
-10
C.
16
D.
-16
Correct Answer A. 10
Explanation The answer is 10.Here's how to solve for y in the equation y – 13 = –3:Add 13 to both sides of the equation to isolate y on one side:y – 13 + 13 = –3 + 13Simplify both sides:y = 10Therefore, the solution to the equation y – 13 = –3 is y = 10.
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9.
If p × q = p + q + p/q, the value of 8 × 2 is:
A.
6
B.
10
C.
14
D.
16
Correct Answer C. 14
Explanation To solve for 8 × 2 in the equation p × q = p + q + p/q, we need to plug in the values p = 8 and q = 2:8 × 2 = 8 + 2 + 8/2Now, let's solve the equation step-by-step:Division first: 8/2 = 4Addition: 8 + 2 + 4 = 14Therefore, the value of 8 × 2 in the given equation is 14.The other options are incorrect because:6: This result comes from incorrectly adding before dividing (8 + 2 = 10, then 10/2 = 5).10: This result comes from incorrectly multiplying before dividing (8 + 2 + 8 = 18, then 18/2 = 9).16: This result comes from incorrectly multiplying first (8 * 2 = 16).Remember, in the order of operations (PEMDAS), division and multiplication have the same priority and are done from left to right before addition and subtraction.
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10.
If a * b = 2 (a + b), then 5 * 2 is equal to:
A.
3
B.
10
C.
14
D.
20
Correct Answer C. 14
Explanation In the equation a * b = 2 (a + b), where * represents a custom operation, the answer for 5 * 2 is not directly obtainable using conventional math operations like addition, subtraction, multiplication, or division.To solve for 5 * 2, we need to understand the logic behind the custom operation. Since the operation involves doubling the sum of a and b, it essentially multiplies both a and b by 2 and then adds them together.So, for 5 * 2:Double both 5 and 2: 2 * 5 = 10, 2 * 2 = 4Add the doubled values: 10 + 4 = 14Therefore, 5 * 2 in this custom operation equals 14.The other options are incorrect because:3: This result would be obtained if the operation simply involved multiplying a and b.10: This result would be obtained if the operation only doubled one of the numbers.20: This result is too high and doesn't follow the logic of the custom operation.