Martha's solution to the inequality $8x + 5 \leq 3x - 10$ is shown on the number line - OCR - GCSE Maths - Question 9 - 2019 - Paper 6
Question 9
Martha's solution to the inequality $8x + 5 \leq 3x - 10$ is shown on the number line.
Is her solution correct?
Explain your reasoning.
Worked Solution & Example Answer:Martha's solution to the inequality $8x + 5 \leq 3x - 10$ is shown on the number line - OCR - GCSE Maths - Question 9 - 2019 - Paper 6
Step 1
Determine the inequality: $8x + 5 \leq 3x - 10$
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Answer
To solve for x, first isolate the variable. Subtract 3x from both sides:
8x−3x+5≤−10
This simplifies to:
5x+5≤−10
Next, subtract 5 from both sides:
5x≤−15
Finally, divide by 5:
x≤−3
Step 2
Check the number line
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Answer
Martha's number line shows a shaded region to the left of -3, including -3 with a closed dot. This represents the set of all x values such that x≤−3, which is correct.
Step 3
Conclusion
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Answer
Martha's solution is correct as it accurately shows the inequality x≤−3. Therefore, her representation on the number line correctly reflects the solution to the inequality.
