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Linear Equations and Inequalities Practice Tests

These Grade 9 Math practice tests cover one-step and multi-step linear equations, variables on both sides, identities, contradictions, fractions, decimals, compound inequalities, absolute value, number-line graphs, literal equations, formulas, and real-world models.

Skills covered

  • Solving equations with distribution, fractions, decimals, and variables on both sides
  • Recognizing identities, contradictions, no-solution equations, and infinitely many solutions
  • Solving and graphing one-variable, compound, and absolute-value inequalities
  • Rearranging formulas and interpreting slope, rate, cost, distance, and budget models
  • Checking solutions and translating geometric, ticket, work, travel, and number problems

How to use these practice tests

Simplify both sides first, perform the same operation on both sides, reverse the inequality sign when multiplying or dividing by a negative number, and substitute the final answer into the original equation or model.

For more Grade 9 Math practice, return to the Grade 9 Math category.

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Grade 9 Linear Equations and Inequalities Practice Tests

Practice Grade 9 Math questions about multi-step linear equations, equations with variables on both sides, inequalities, absolute value, formulas, and algebraic models.

Choose the best answer. Keep equations balanced, reverse an inequality when dividing by a negative, show formula steps, and verify the result in context.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Solve y=mx+by=mx+b for m, assuming x is not zero.

Please select an answer first.

Correct answer: A

The correct answer is y−bx\frac{y-b}{x}.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Subtract b from both sides and divide by x: m = (y - b)/x.
  3. Check the conclusion: The correct choice is y−bx\frac{y-b}{x}.

Subtract b from both sides and divide by x: m = (y - b)/x.

2. QuestionMultiple choice

Solve A=lwA=lw for w, assuming l is not zero.

Please select an answer first.

Correct answer: B

The correct answer is Al\frac{A}{l}.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Divide both sides by l to isolate w: w = A/l.
  3. Check the conclusion: The correct choice is Al\frac{A}{l}.

Divide both sides by l to isolate w: w = A/l.

3. QuestionMultiple choice

Solve P=2l+2wP=2l+2w for l.

Please select an answer first.

Correct answer: C

The correct answer is P−2w2\frac{P-2w}{2}.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Subtract 2w and divide by 2: l = (P - 2w)/2.
  3. Check the conclusion: The correct choice is P−2w2\frac{P-2w}{2}.

Subtract 2w and divide by 2: l = (P - 2w)/2.

4. QuestionMultiple choice

Solve d=rtd=rt for t, assuming r is not zero.

Please select an answer first.

Correct answer: D

The correct answer is dr\frac{d}{r}.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Divide both sides by r to isolate time: t = d/r.
  3. Check the conclusion: The correct choice is dr\frac{d}{r}.

Divide both sides by r to isolate time: t = d/r.

5. QuestionMultiple choice

Use F=95C+32F=\frac{9}{5}C+32. What is F when C = 20?

Please select an answer first.

Correct answer: A

The correct answer is 68.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Substitute 20: F = (9/5)(20) + 32 = 36 + 32 = 68.
  3. Check the conclusion: The correct choice is 68.

Substitute 20: F = (9/5)(20) + 32 = 36 + 32 = 68.

6. QuestionMultiple choice

A cost model is C=2.5n+10C=2.5n+10. How many items can be bought when C = 35?

Please select an answer first.

Correct answer: B

The correct answer is 10.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Substitute 35: 35 = 2.5n + 10, so 25 = 2.5n and n = 10.
  3. Check the conclusion: The correct choice is 10.

Substitute 35: 35 = 2.5n + 10, so 25 = 2.5n and n = 10.

7. QuestionMultiple choice

What is the slope through (2, 5) and (6, 13)?

Please select an answer first.

Correct answer: C

The correct answer is 2.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: The slope is (13 - 5)/(6 - 2) = 8/4 = 2.
  3. Check the conclusion: The correct choice is 2.

The slope is (13 - 5)/(6 - 2) = 8/4 = 2.

8. QuestionMultiple choice

A line is modeled by y=12+4xy=12+4x. What is x when y = 32?

Please select an answer first.

Correct answer: D

The correct answer is 5.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Substitute y = 32: 32 = 12 + 4x, so 20 = 4x and x = 5.
  3. Check the conclusion: The correct choice is 5.

Substitute y = 32: 32 = 12 + 4x, so 20 = 4x and x = 5.

9. QuestionMultiple choice

A budget is modeled by 3x+5≤203x+5\le20. What is the greatest whole-number x?

Please select an answer first.

Correct answer: A

The correct answer is 5.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Subtract 5 and divide by 3: x ≤ 5, so the greatest whole-number value is 5.
  3. Check the conclusion: The correct choice is 5.

Subtract 5 and divide by 3: x ≤ 5, so the greatest whole-number value is 5.

10. QuestionMultiple choice

An $80 item is discounted by 25%. What is the sale price?

Please select an answer first.

Correct answer: B

The correct answer is $60.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: A 25% discount is $20, so subtracting it from $80 gives a sale price of $60.
  3. Check the conclusion: The correct choice is $60.

A 25% discount is $20, so subtracting it from $80 gives a sale price of $60.

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