Find the range of values of x which satisfies −232≤x+31<331;x∈RGraph these values of x on the number line.

Given, −232≤x+31<331;x∈R−232≤x+31 and x+31<331⇒−38≤x+31 and x+31<310⇒−38−31≤x and x<310−31⇒−39≤x and x<39⇒−3≤x and x<3Therefore, −3≤x<3 And the required graph of the solution set is given in figure.

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Find the range of values of x which satisfies -2 {2}{3} x+{1}

Question

Find the range of values of $x$ which satisfies
$- 2 \frac{2}{3} \leq x + \frac{1}{3} < 3 \frac{1}{3}; x \in R$
Graph these values of $x$ on the number line.

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Find the range of values of

x

which satisfies

- 2 \frac{2}{3} \leq x + \frac{1}{3} < 3 \frac{1}{3}; x \in R

Graph these values of

x

on the number line.

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Text solutionVerified

Given,

- 2 \frac{2}{3} \leq x + \frac{1}{3} < 3 \frac{1}{3}; x \in R

- 2 \frac{2}{3} \leq x + \frac{1}{3}

and

x + \frac{1}{3} < 3 \frac{1}{3}

\Rightarrow - \frac{8}{3} \leq x + \frac{1}{3}

and

x + \frac{1}{3} < \frac{10}{3}

\Rightarrow - \frac{8}{3} - \frac{1}{3} \leq x

and

x < \frac{10}{3} - \frac{1}{3}

\Rightarrow - \frac{9}{3} \leq x

and

x < \frac{9}{3}

\Rightarrow - 3 \leq x

and

x < 3

Therefore,

- 3 \leq x < 3

And the required graph of the solution set is given in figure.

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Question Text	Find the range of values of $x$ which satisfies $- 2 \frac{2}{3} \leq x + \frac{1}{3} < 3 \frac{1}{3}; x \in R$ Graph these values of $x$ on the number line.
Answer Type	Text solution:1
Upvotes	150

Find the range of values of x which satisfies −232​≤x+31​<331​;x∈RGraph these values of x on the number line.

Text solutionVerified

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Find the range of values of $x$ which satisfies
$- 2 \frac{2}{3} \leq x + \frac{1}{3} < 3 \frac{1}{3}; x \in R$
Graph these values of $x$ on the number line.