Question 1.<br />(a) Find the value of x, which satisfy the inequation.<br />-2 < } - $ 2, x €w.<br />Graph the solution set on the number line.
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Solve the following inequation and graph the solution set on the number line. 2x−3<x+2≤3x+5,xϵR.
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2x−3<x+2≤3x+5
Let's break this up into two parts.....
First.......
2x−3<x+2 ........ (add 3 to both sides)
2x<x+5 ........ (subtract x from both sides)
x<5
Secondly.......
x+2≤3x+5
(subtract 5 from both sides)
x−3≤3x ......... (subtract x from both sides)
−3<=2x ....... (divide both sides by 2)
−3≤2x (which also means x≥−
2
3
)
Thus.........−
2
3
≤x<5
Or in interval notation...... [−
2
3
,5)
Try picking some values "outside" this interval. You'll find that they won't satisfy both inequalities!!
Step-by-step explanation:
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