Question

The number line below represent the solution set of which of the following equation?


A). -13 < 1 – 2x ≤ -3

B). 3 < 2x - 1 ≤ 15

C). -13 ≤ 1 – 2x < -3

D). 3 ≤ 2x - 1 < 15

Answer 1

Answer:

Given: −

3

x

≤

2

x

−1

3

1

<

6

1

Taking L.C.M. of 3,2 and 6 is 6.

−

3

x

×6≤

2

x

×6−

3

4

×6<

6

1

×6

−2x≤3x−8<1

⇒−2x≤3x−8 and 3x−8<1

⇒8≤3x+2x ⇒3x<1+8

⇒8≤5x ⇒3x<9

⇒

5

8

≤x ⇒x<3

∴ The solution set is {x:1.6≤x≤3,xϵR}

hope it helps ☺️

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Answer 2

The set of the solution is

$2 \leqslant x < 7$

as represented on number line So,

$-13 < 1 - 2x \leqslant -3$

multiply with -1 in inequality we get,

$13 > - 1 + 2x \geqslant 3$

Add with 1 in inequality we get,

$14 > 2x \geqslant 4$

Divide by 2 we get

$7 > x \geqslant 2$

as we see here this set of solution is our given set so,

option A is our solution.