Inequalities and Formula Rearrangement in Algebra

1. Sarah has 3x + 5y and 2x + 3y. Combine like terms to find the total expression.

• 4x + 7y

• 3x + 8y

• 5x + 8y

• 6x + 5y

2. If the square root of a number is 7, what is the value of the number?

• 14

• 64

• 49

• 36

3. A store sells pencils for x cents each. If you buy more than 10 pencils, you spend more than 2 dollars. Create an inequality to represent this situation.

• n * x > 100 for n > 5

• n * x < 200 for n < 10

• n * x = 200 for n = 10

• n * x > 200 for n > 10

4. Rearrange the formula A = lw (area of a rectangle) to solve for l in terms of A and w.

• l = A + w

• l = A * w

• l = A / w

• l = A - w

5. The sum of a number and 12 is less than 30. Write an inequality to represent this situation and solve for the number.

• x = 18

• x < 18

• x > 30

• x < 12

6. Factor the expression 2x^2 + 8x.

• 2x(x + 4)

• x(2x + 8)

• 2x^2 + 4x + 4

• 2(x^2 + 4x)

7. If the square root of x is equal to 4, what is the value of x?

• 12

• 8

• 20

• 16

8. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an inequality to represent the total cost if you want to spend less than $100.

• 50 + 0.20m < 100

• 0.20m < 50

• 50 + 0.20m = 100

• 50 + 0.20m > 100

9. Rearrange the formula C = 2πr (circumference of a circle) to solve for r in terms of C.

• r = C / (π^2)

• r = 2C / π

• r = C / π

• r = C / (2π)

10. If 5x - 3 = 2x + 12, solve for x and check your solution.

• 3

• 7

• 5

• 10