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Algebra

Question 4 of 8

Linear & Quadratic Inequalities

Question

Find the set of values of \(x\) for which \(4x - 4(x + 2) \lt 3(2 - x)\)

Show solution Hide solution Fully worked — 7 steps
  1. Multiply \(-4\) and \((x + 2)\); \(3\) and \((2 - x)\)
    \[ 4x - 4(x + 2) \lt 3(2 - x) \]
    \[ 4x - 4x - 8 \lt 6 - 3x \]
  2. Combine similar terms
    \[ -8 \lt 6 - 3x \]
  3. Add \(3x\) and \(8\) to both sides
    \[ -8 + 3x + 8 \lt 6 - 3x + 3x + 8 \]
  4. Combine similar terms
    \[ 3x \lt 14 \]
  5. Divide both sides by \(3\)
    \[ x \lt \frac{14}{3} \]
  6. In graph

    On the number line, an open circle at \(\dfrac{14}{3}\) with a ray extending to the left shows the solution set: every value of \(x\) less than \(\dfrac{14}{3}\). The circle is open because \(\dfrac{14}{3}\) itself is not included.

    Number line graph of the solution set x < 14/3
  7. Solution set

    \(\therefore\) the solution set of the inequality \(4x - 4(x + 2) \lt 3(2 - x)\) is \(x \lt \dfrac{14}{3}\). That is, the solution set is every value of \(x\) less than \(\dfrac{14}{3}\).