Solve the inequality
$-2 < 5x + 3 < 18, x \in \mathbb{R}$.
(i) To solve the compound inequality, we will break it down into two parts:
1. First, solve the left ... show full transcript
Worked Solution & Example Answer:Solve the inequality
$-2 < 5x + 3 < 18, x \in \mathbb{R}$ - Junior Cycle Mathematics - Question 12 - 2014
Step 1
Solve the inequality $-2 < 5x + 3 < 18, x \in \mathbb{R}$
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Answer
To solve the compound inequality, we will break it down into two parts:
First, solve the left part of the inequality:
−2<5x+3
Subtract 3 from both sides:
−5<5x
Now divide both sides by 5:
−1<x
Next, solve the right part of the inequality:
5x+3<18
Subtract 3 from both sides:
5x<15
Divide both sides by 5:
x<3
Combining these results, we have the solution:
−1<x<3
Step 2
Graph your solution on the number line below.
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Answer
On the number line, draw an open circle at -1 and an open circle at 3. Shade the region between -1 and 3 to indicate the solution to the inequality.
Step 3
Write down an inequality in x to show the range of cash she could spend in the shop.
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Answer
The range of cash Niamh could spend is given by:
25≤x≤50
Step 4
Write down an inequality in y to show the price range of articles she could buy.
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Answer
The price range of articles Niamh could buy is:
35≤y≤60
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