CHALLENGE 18 problems

Question

for fun

1. Simplify: 3x + 7 + 2x – 5

2. Evaluate: 4(2x + 3) – 5x

3. Solve: 2x/5 = 8

4. Find the value of x: 3(x – 5) = 21

5. Simplify: 2(3x + 4) – 5(x – 2)

6. Solve for x: 4x + 7 = 3x – 2

7. Evaluate: 2(3x – 5) + 4(x + 2)

8. Find the perimeter of a rectangle with length 2x and width 3x

9. Simplify: 5(x + 2) – 2(3x – 4)

10. Find the area of a square with side length 4x

11. Determine the slope of the line passing through the points (2, 3) and (4, 7)

12. Solve: 3(x + 2) = 2x – 5

13. Find the x-intercept of the line 2x + 3y = 12

14. Simplify: 2(x + 3) + 3(2x – 1)

15. Solve for x: 5x + 8 = 3x – 4

16. Evaluate: 3(2x – 4) + 5(x + 3)

17. Find the value of y: 2x + 4y = 10

18. Determine if the point (3, 6) lies on the line 4x – 2y = 10

Answer 1

Without giving you the exact answer for all of these, here is how to work through them:

1) 3x+7+2x-5

Step 1: Combine like terms. Since the terms with x's in them (3x and 2x) both have x¹ in them, we can add these together. Since there are also constants, we can combine those as well. We add the 3x and 2x together, then we combine the 7-5, and we get:

Answer: 5x+2

2) 4(2x+3)-5x

Step 1: Distribute. Whenever we have something being multiplied by a parentheses, we can distribute. We first distribute the 4 to the 2x, and then to the +3. By distributing (multiplying) the 4 to the 2x we get 8x, and by distributing the 4 to the +3 we get 12.

8x+12-5x

Step 2: We now need to look for like terms that we can combine. As we only have one constant here (12), it gets left alone. We do have two terms with x¹ in them, so we can combine these. 8x-5x is going to give us 3x, as 8-5=3.

Answer: 3x+12

The same general process can be used for questions 3 through 7, as well as 9, 12, 14, 15, 16.

For question 8: First, how do we find the perimeter of a rectangle? We must add all of the side lengths together. Perimeter describes the outside of a shape, so we add up all of the sides. Thus if the width is 3x and length is 2x, we must draw a rectangle with 3x written twice, and 2x written twice, and then add them all together.

Question 10: How do we find the area of a square? All of the side lengths of a square are the same, so this tells us that our length is going to be 4x and our width will be 4x as well. This means that all we have to do is multiple these together to find the total area.

Question 11: The formula for slope is m= ( y₂ - y₁) / (x₂-x₁). Slope is represented by m in this equation. Thus, if we take our second y value and subtract the first y value from it, we get the numerator, or top of the fraction. Then we take the 2nd x value and subtract the 1st x value from it, giving us the denominator, or bottom of the fraction. These can then be divided to find the slope.

Q13: To find the x intercept, one must plug in a 0 for y, and then solve for x. So plug in a 0 for y, and then get x completely by itself by dividing both sides by 2, and you will get your answer!

Q18: To find out if a point lies on a line, we must plug that point in to the equation. Therefore, 3 will get plugged in for x and 6 will get plugged in for y. If the point is on the line, you will end up with a true equation. This means it will come out to something like 5=5 or 22=22. If you get something like 6=24, which we know is not true, then the point is not on the line.