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Algebra

Question 2 of 8

Linear & Quadratic Inequalities

Question

Find the set of values of \(x\) for which \(4(2x - 5) \leq 10x + 8\)

Show solution Hide solution Fully worked — 6 steps
  1. Multiply \(4\) and \((2x - 5)\)
    \[ 4(2x - 5) \leq 10x + 8 \]
    \[ 8x - 20 \leq 10x + 8 \]
  2. Subtract \(10x\) from and add \(20\) to both sides
    \[ 8x - 20 - 10x + 20 \leq 10x + 8 - 10x + 20 \]
  3. Combine similar terms
    \[ -2x \leq 28 \]
  4. Divide both sides by \(-2\)
    \[ x \geq -14 \]

    (note: the direction of the inequality will reverse because it was divided by a negative number)

  5. In graph

    On the number line, a filled circle at \(-14\) with a ray extending to the right shows the solution set: every value of \(x\) greater than or equal to \(-14\). The circle is filled because \(-14\) itself is included.

    Number line graph of the solution set x ≥ −14
  6. Solution set

    \(\therefore\) the solution set of the inequality \(4(2x - 5) \leq 10x + 8\) is \(x \geq -14\). That is, the solution set is every value of \(x\) greater than or equal to \(-14\).