Standard High contrast

Algebra

Question 3 of 8

Linear & Quadratic Inequalities

Question

Find the set of values of \(x\) for which \(2(4x + 3) \geq 5 - 4(x - 1)\)

Show solution Hide solution Fully worked — 7 steps
  1. Multiply \(2\) and \((4x + 3)\); \(-4\) and \((x - 1)\)
    \[ 2(4x + 3) \geq 5 - 4(x - 1) \]
    \[ 8x + 6 \geq 5 - 4x + 4 \]
  2. Combine similar terms
    \[ 8x + 6 \geq 9 - 4x \]
  3. Add \(4x\) to and subtract \(6\) from both sides
    \[ 8x + 6 + 4x - 6 \geq 9 - 4x + 4x - 6 \]
  4. Combine similar terms
    \[ 12x \geq 3 \]
  5. Divide both sides by \(12\) then simplify
    \[ x \geq \frac{1}{4} \]
  6. In graph

    On the number line, a filled circle at \(\dfrac{1}{4}\) with a ray extending to the right shows the solution set: every value of \(x\) greater than or equal to \(\dfrac{1}{4}\). The circle is filled because \(\dfrac{1}{4}\) itself is included.

    Number line graph of the solution set x ≥ 1/4
  7. Solution set

    \(\therefore\) the solution set of the inequality \(2(4x + 3) \geq 5 - 4(x - 1)\) is \(x \geq \dfrac{1}{4}\). That is, the solution set is every value of \(x\) greater than or equal to \(\dfrac{1}{4}\).