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Determine the solution for the inequality: 3(x - 1) < 2(x + 2).

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Question: Determine the solution for the inequality: 3(x - 1) < 2(x + 2).

Options:

  1. x < 5
  2. x > 5
  3. x < 1
  4. x > 1

Correct Answer: x < 5

Solution: 

Step 1: Expand: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.

Determine the solution for the inequality: 3(x - 1) < 2(x + 2).

Practice Questions

Q1
Determine the solution for the inequality: 3(x - 1) < 2(x + 2).
  1. x < 5
  2. x > 5
  3. x < 1
  4. x > 1

Questions & Step-by-Step Solutions

Determine the solution for the inequality: 3(x - 1) < 2(x + 2).
  • Step 1: Expand both sides of the inequality. Multiply 3 by (x - 1) to get 3x - 3. Multiply 2 by (x + 2) to get 2x + 4. Now the inequality is 3x - 3 < 2x + 4.
  • Step 2: To get all the x terms on one side, subtract 2x from both sides. This gives you 3x - 2x - 3 < 4, which simplifies to x - 3 < 4.
  • Step 3: Now, to isolate x, add 3 to both sides of the inequality. This results in x < 7.
  • Inequalities – Understanding how to manipulate and solve inequalities involving variables.
  • Algebraic Expansion – Applying the distributive property to expand expressions.
  • Isolating Variables – Rearranging the inequality to isolate the variable on one side.
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