Priya is comparing two supplier quotes for sturdy cardboard delivery boxes before choosing the cheaper option for her family's corner shop ahead of the busy...
Question 1 Report
Priya is comparing two supplier quotes for sturdy cardboard delivery boxes before choosing the cheaper option for her family's corner shop ahead of the busy Christmas trading period, and after adding up the totals herself needs to solve the inequality \(5(x - 2) < 3(x + 4)\).
- Solve this inequality. (3)
- Illustrate your solution using the number line shown. (2)
Answer Details
This question tests solving a linear inequality with brackets on both sides and illustrating the solution on a number line.
- Expand both brackets: \(5(x - 2) < 3(x + 4)\) becomes \(5x - 10 < 3x + 12\). Subtract \(3x\) from both sides: \(2x - 10 < 12\). Add 10: \(2x < 22\). Divide by 2: \(x < 11\). [3]
- Since \(x\) is strictly less than 11, an open circle is drawn at 11, with the line shaded to the left. [2]
Exam tip: expand each bracket completely and collect all the unknown terms on one side before dividing; doing this in a clear, separate line of working (as above) avoids losing method marks even if the final answer slips.
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