Question
Solve the following inequation, write the solution set and represent it on the number line.
$-3(x-7) \geq 15-7 x>\frac{x+1}{3}, x \in R$
$-3(x-7) \geq 15-7 x>\frac{x+1}{3}, x \in R$
✓
Answer
$\Rightarrow 3(x-7) \geq 15-7 x>\frac{x+1}{3}, x \in R $
$ \Rightarrow-3(x-7) \geq 15-7 x \text { and } 15-7 x>\frac{x+1}{3} $$\Rightarrow-3 x+21 \geq 15-21 \text { and } 45-1>x+21 x $
$ \Rightarrow 4 x \geq-6 \text { and } 44>22 x $
$ \Rightarrow x \geq \frac{-3}{2} \text { and } 2>x $
$ \Rightarrow x \geq-1.5 \text { and } 2>x$
The solution set is $\{x: x \in R,-1.5 \leq x<2\}$
The solution set is represented on number line as follows:
$ \Rightarrow-3(x-7) \geq 15-7 x \text { and } 15-7 x>\frac{x+1}{3} $$\Rightarrow-3 x+21 \geq 15-21 \text { and } 45-1>x+21 x $
$ \Rightarrow 4 x \geq-6 \text { and } 44>22 x $
$ \Rightarrow x \geq \frac{-3}{2} \text { and } 2>x $
$ \Rightarrow x \geq-1.5 \text { and } 2>x$
The solution set is $\{x: x \in R,-1.5 \leq x<2\}$
The solution set is represented on number line as follows:
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