Grade: 9 Subject: Math (Algebra I) Unit: Linear Equations & Inequalities Lesson: 6 of 6 SAT: Algebra ACT: Math

Unit Quiz

Instructions

This quiz covers all topics from the Linear Equations & Inequalities unit:

Try to complete all problems before checking your answers.

Question 1: Solve for x: 4x - 7 = 2x + 9

Answer: x = 8

Solution: Subtract 2x: 2x - 7 = 9. Add 7: 2x = 16. Divide by 2: x = 8.

Question 2: Solve for x: 3(2x - 4) + 5 = 23

Answer: x = 5

Solution: Distribute: 6x - 12 + 5 = 23. Simplify: 6x - 7 = 23. Add 7: 6x = 30. Divide: x = 5.

Question 3: Solve the inequality: 2x + 5 < 13

Answer: x < 4

Solution: Subtract 5: 2x < 8. Divide by 2: x < 4.

Question 4: Solve the inequality: -3x + 6 >= 15

Answer: x <= -3

Solution: Subtract 6: -3x >= 9. Divide by -3 (flip sign): x <= -3.

Question 5: The perimeter of a rectangle is 56 inches. The length is 4 inches more than the width. Find the length.

Answer: Length = 16 inches

Solution: Let w = width, l = w + 4. Perimeter: 2w + 2(w+4) = 56. Solve: 4w + 8 = 56, w = 12. Length = 16.

Question 6: Solve for x: (x - 3)/4 + 2 = 5

Answer: x = 15

Solution: Subtract 2: (x-3)/4 = 3. Multiply by 4: x - 3 = 12. Add 3: x = 15.

Question 7: Three times a number minus 8 equals the number plus 10. Find the number.

Answer: 9

Solution: Let x = number. Equation: 3x - 8 = x + 10. Subtract x: 2x - 8 = 10. Add 8: 2x = 18. x = 9.

Question 8: Solve: 5(x + 2) = 3(x - 2) + 4x

Answer: x = 8

Solution: Distribute: 5x + 10 = 3x - 6 + 4x. Simplify right side: 5x + 10 = 7x - 6. Subtract 5x: 10 = 2x - 6. Add 6: 16 = 2x. x = 8.

Question 9: Write and solve: A taxi charges $3 plus $2.50 per mile. If the total is $18, how many miles?

Answer: 6 miles

Solution: Let m = miles. Equation: 3 + 2.50m = 18. Subtract 3: 2.50m = 15. Divide: m = 6.

Question 10: Solve for x: 2(x - 1) - 3(x + 2) = -11

Answer: x = 3

Solution: Distribute: 2x - 2 - 3x - 6 = -11. Combine: -x - 8 = -11. Add 8: -x = -3. Multiply by -1: x = 3.