Question

List the solution set and represent it on a number line.

1.)
50-2(x-5)<25, x belongs to W.

2.)
$- 3 < - \frac{1}{2} - \frac{2x}{3} \leqslant \frac{5}{6}$x belongs to R

3.)
$- 3(x - 7) \geqslant 15 - 7x > \frac{x + 1}{3}$
x belongs to R


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Answer 1

Solution :-

1.)  50 - 2(x-5) < 25, x belongs to W.

50 - 2x + 10 < 25

60 - 2x < 25

- 2x < 25 - 60

- 2x < - 35

2x > 35

x > $\dfrac{35}{2}$

Solution :- {x: x > $\dfrac{35}{2}$, where x ∈ W}

2.)  $-3<-\dfrac{1}{2} - \dfrac{2x}{3} \leq \dfrac{5}{6}$, x belongs to R

$-3< \dfrac{-3-4x}{6} \leq \dfrac{5}{6}$

$-3< \dfrac{-3-4x}{6}\:\:\:and\:\:\: \dfrac{-3-4x}{6} \leq \dfrac{5}{6}$

$-3\times 6<{-3-4x}\:\:\:and\:\:\: -3-4x \leq \dfrac{5}{6}\times 6\\\\-18<{-3-4x}\:\:\:and\:\:\: -3-4x \leq 5\\\\-18+ 3<-4x\:\:\:and\:\:\: -4x \leq 5+3\\\\-15<-4x\:\:\:and\:\:\: -4x \leq 8\\\\15>4x\:\:\:and\:\:\: 4x \geq 8\\\\\dfrac{15}{4}>x\:\:\:and\:\:\: x \geq \dfrac{8}{4}\\\\\dfrac{15}{4}>x\:\:\:and\:\:\: x \geq2$

Solution :- {x: 2$\geg$$\leq$ x <  $\dfrac{15}{4}$, where x ∈ R}

3.)  $-3(x-7) \geq 15-7x>\dfrac{x+1}{3}$, x belongs to R

$-3x+21 \geq 15-7x>\dfrac{x+1}{3}\\\\-3x+21 \geq 15-7x\:\:\:and\:\:\:15-7x>\dfrac{x+1}{3}\\\\21-15 \geq -7x+3x\:\:\:and\:\:\:3(15-7x)>x+1\\\\6 \geq -4x\:\:\:and\:\:\:45-21x>x+1\\\\-6 \leq 4x\:\:\:and\:\:\:45-1>x+21x\\\\\dfrac{-6}{4}\leq x\:\:\:and\:\:\:44>22x\\\\\dfrac{-3}{2}\leq x\:\:\:and\:\:\:\dfrac{44}{22}>x\\\\\dfrac{-3}{2}\leq x\:\:\:and\:\:\:2>x$

Solution :- {x: $\dfrac{-3}{2}$$\geg$$\leq$ x < 2, where x ∈ R}

All the number lines are in the attachment.