At a music festival, the number of people \(x\) allowed into a viewing pen must satisfy \(4x - 5 \geq 2x + 11\). The number line below is drawn for your ans...
Question 1 Report
At a music festival, the number of people \(x\) allowed into a viewing pen must satisfy \(4x - 5 \geq 2x + 11\). The number line below is drawn for your answer.
- Solve the inequality. (1)
- Show your solution on the number line. (1)
Answer Details
(a) Solve \(4x - 5 \geqslant 2x + 11\) by collecting the \(x\) terms on one side.
- Subtract \(2x\) from both sides and add 5 to both sides: \(4x - 2x \geqslant 11 + 5\), that is \(2x \geqslant 16\), so \(x \geqslant 8\). Dividing by the positive number 2 leaves the direction of the inequality unchanged. [1]
(b) Because the inequality is \(\geqslant\), the value 8 is included, which is shown by a filled circle at 8, with the line shaded to the right to represent every value greater than 8.
The filled circle earns the mark only if it is at 8 and solid; a hollow circle would represent \(x > 8\) and would exclude a pen holding exactly 8 people, which the inequality allows. [1]
Check the boundary in the original inequality: at \(x = 8\), \(4\times 8 - 5 = 27\) and \(2\times 8 + 11 = 27\), so the two sides are equal, confirming that 8 belongs to the solution set.
Download The App On Google Playstore
Everything you need to excel in your exams
