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Solve the following inequality and show the solution on the number line - Junior Cycle Mathematics - Question Question - 2014

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Solve the following inequality and show the solution on the number line. $$-17 \leq 1 - 3x < 13$$ $x \in \mathbb{Z}$

Worked Solution & Example Answer:Solve the following inequality and show the solution on the number line - Junior Cycle Mathematics - Question Question - 2014

Step 1

-17 \leq 1 - 3x

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Answer

To solve the inequality, we first isolate the term involving x:

  1. Subtract 1 from both sides: −17−1≤−3x-17 - 1 \leq -3x −18≤−3x-18 \leq -3x

  2. Divide by -3 (remember to reverse the inequality): −18−3≥x\frac{-18}{-3} \geq x 6≥x6 \geq x or equivalently, x≤6x \leq 6.

Step 2

1 - 3x < 13

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Answer

Next, we solve the second part of the inequality:

  1. Subtract 1 from both sides: −3x<12-3x < 12

  2. Divide by -3 (again reversing the inequality): x>−4x > -4.

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