On the grid show, by shading, the region that satisfies all of these inequalities - Edexcel - GCSE Maths - Question 18 - 2021 - Paper 1
Question 18
On the grid show, by shading, the region that satisfies all of these inequalities.
2y + 4 < x < 3
y < 6 - 3x
Label the region R.
Worked Solution & Example Answer:On the grid show, by shading, the region that satisfies all of these inequalities - Edexcel - GCSE Maths - Question 18 - 2021 - Paper 1
Step 1
Step 1: Solve the inequality 2y + 4 < x
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Answer
To express the inequality in terms of y, rearrange it:
2y<x−4y<2x−4
This equation represents a straight line with a slope of 1/2 and a y-intercept of -2.
Step 2
Step 2: Solve the inequality y < 6 - 3x
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Answer
This equation can be rearranged to find y:
y<6−3x
This line has a slope of -3 and a y-intercept of 6.
Step 3
Step 3: Graph the inequalities and shade the appropriate region
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Answer
Draw the line for the first inequality, using dotted lines to show that the points on the line are not included.
Draw the line for the second inequality similarly.
The valid region that satisfies both inequalities is below both lines. Shade this region on the grid and label it R.
