Basic Algebra Quiz Questions With Solutions

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1. If 3x + 5 = 14, what is the value of x?

Think of this equation like a balanced scale. To find "x," we need to get it alone on one side. First, we subtract 5 from both sides to keep things balanced (3x = 9). Then, we divide both sides by 3, like splitting the weight equally, to find that x = 3.

Explanation

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About This Quiz

Basic Algebra Quiz Questions With Solutions - Quiz

Welcome to our Basic Algebra Quiz! Whether you're a student looking to sharpen your algebraic skills or someone who enjoys the challenge of mathematical puzzles, this quiz is... see moredesigned to test and enhance your knowledge of basic 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 multiple topics, from solving equations to working with variables, expressions, and inequalities. Do you know the tips and tricks to solve algebra? This basic algebra quiz will test your ability to solve basic Algebra problems. We have curated a variety of questions that will help you practice basic algebra concepts. If you have studied it well, this algebra quiz will be perfect. All the best! Remember to share the quiz with others who wish to practice this mathematical concept. Whether preparing for an algebra test, brushing up on your math skills, or enjoying the mental exercise, this quiz is an excellent resource. Are you ready to dive into algebra and expand your mathematical knowledge? Let's get started! see less

2. 7 + 2x = 15 What is the value of x?

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 = 8

Divide both sides by 2: 2x / 2 = 8 / 2 x = 4

Therefore, x = 4 is the only solution to the equation.

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 = 8

Divide both sides by 2: 2x / 2 = 8 / 2 x = 4

Therefore, x = 4 is the only solution to the equation.

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3. Ben pays $40 per month to attend a weekly yoga class. His sister Ilene 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?

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.

Explanation

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4. Solve for y in the equation: y – 13 = –3

-10

-16

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 + 13

Simplify both sides:

y = 10

Therefore, the solution to the equation y – 13 = –3 is y = 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 + 13

Simplify both sides:

y = 10

Therefore, the solution to the equation y – 13 = –3 is y = 10.

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5. Y = 27j - 7 - 7j. If y = 13 what will j be equal to?

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.

Explanation

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6. Simplify the expression: 4(2x - 3) + 2(x + 5)

10x - 2

10x + 2

8x - 2

8x + 2

Imagine this expression as a recipe with ingredients to combine. First, we "distribute" the 4 and 2, multiplying them with the terms inside the parentheses. This gives us 8x - 12 + 2x + 10. Then, we combine the "x" terms and the number terms separately, like grouping similar ingredients, to get 10x - 2.

Explanation

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7. Solve for y: 2(y - 4) = 3(y + 2)

-14

-10

This equation is like a puzzle where we need to uncover the value of "y." We start by distributing the 2 and 3 on each side, giving us 2y - 8 = 3y + 6. Then, we move the "y" terms to one side and the numbers to the other, keeping the equation balanced. This leads us to the solution: y = -14.

Explanation

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8. Y = 7x + 3 Where does this line cross the y-axis?

(0,3)

(1,2)

(7,3)

(3,7)

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).

Explanation

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9. If a rectangle has a length of (x + 3) and a width of (x - 2), what is its area?

2x + 1

X^2 + x - 6

X^2 + 5x - 6

2x + 6

Imagine a rectangle with sides that have unknown lengths (represented by "x"). To find the area, we multiply the length and width. So, we multiply (x + 3) and (x - 2). This involves some careful expansion (like FOILing), and after combining terms, we get the area: x^2 + x - 6.

Explanation

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10. What is the slope of the line represented by the equation y = -2x + 5?

-2

-5

This equation is like a secret code for a line on a graph. The "-2" in front of the "x" tells us how steep the line is (its slope). The bigger the number, the steeper the line. In this case, the slope is -2, meaning the line goes downhill as you move from left to right.

Explanation

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11. 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?

Willie will catch him 10 miles before the border.

Robin reaches the border exactly as Willie catches up to her.

No, Robin will spend 25 years in a federal prison.

Yes, Robin will spend his years rich, sitting on a beach.

Explanation

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12. If a * b = 2 (a + b), then 5 * 2 is equal to:

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 = 4
Add the doubled values: 10 + 4 = 14

Therefore, 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.

Explanation

So, for 5 * 2:

Double both 5 and 2: 2 * 5 = 10, 2 * 2 = 4
Add the doubled values: 10 + 4 = 14

Therefore, 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.

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13. If p m q = p + q + p/q, the value of 8 m 2 is:

Explanation

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14. What is the slope of a straight line that connects the following points.
(1,2) & (4,11)

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 / 3

Slope = 3

Therefore, 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).

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 / 3

Slope = 3

Therefore, 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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15. F(x) = 17x - 30 Find f(2) - f(1)

To find f(2) - f(1), we need to evaluate the function f(x) at x = 2 and x = 1, and then subtract the results.

Step 1: Find f(2)

Substitute x = 2 into the function: f(2) = (17 * 2) - 30 f(2) = 34 - 30 f(2) = 4

Step 2: Find f(1)

Substitute x = 1 into the function: f(1) = (17 * 1) - 30 f(1) = 17 - 30 f(1) = -13

Step 3: Calculate f(2) - f(1)

Subtract f(1) from f(2): f(2) - f(1) = 4 - (-13) f(2) - f(1) = 4 + 13 f(2) - f(1) = 17

Therefore, f(2) - f(1) = 17.

Explanation