➕ Algebra 1 · Equations

Solving Two-Step Equations: true or false

Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.

All statements and answers

• In 2x + 3 = 11, the usual first move is to subtract 3 from both sides.

  ✓ True. Subtracting 3 undoes the +3, leaving 2x = 8.

• You only need to subtract from the side that has the variable.

  ✗ False. You must do the same thing to both sides. Otherwise the balance breaks.

• The solution to 3x = 12 is x = 9.

  ✗ False. 3x means 3 times x, so divide by 3: x = 4.

• Addition and subtraction are inverse operations.

  ✓ True. Adding 5 and then subtracting 5 gets you back where you started.

• If 4x − 5 = 11, then x = 4.

  ✓ True. Add 5 to get 4x = 16, then divide by 4. Check: 4(4) − 5 = 11.

• The solution of x/2 + 1 = 5 is x = 10.

  ✗ False. Subtract 1 to get x/2 = 4, then multiply by 2 to get x = 8. The answer 10 comes from multiplying only the 5 by 2 and forgetting the +1.

• Checking by substitution can show that an answer is wrong.

  ✓ True. If the two sides do not match after substituting, the answer is wrong and you should go back and look for the slip.

• The solution to −3x + 5 = −10 is x = −5.

  ✗ False. The solution is x = 5. Check x = −5: −3(−5) + 5 = 20, not −10.

• 2x + 3 = 11 and 2x = 8 have the same solution.

  ✓ True. Subtracting 3 from both sides gives an equivalent equation, so the solution is still x = 4.

• A two-step equation can only have whole-number solutions.

  ✗ False. For example, 2x + 1 = 2 gives x = 1/2.