1.

List the solution set and represent it on a number line.1.)50-2(x-5)

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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.)  -<klux>3</klux>, 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

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.



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