Question
Solving the following inequation, write the solution set and represent it on the number line. $-3(x-$ 7) $\geq 15-7 x >\frac{x+1}{3}, n \in R$
✓
Answer
$
\begin{aligned}
& -3(x-7) \geq 15-7 x>\frac{x+1}{3}, n \in R \\
& -3(x-7) \geq 15-7 x \Rightarrow 3 x+21 \geq 15-7 x \\
& -3 x+7 x \geq 15-21 \Rightarrow 4 x \geq-6 \\
& \Rightarrow x \geq \frac{-6}{4} \\
& \Rightarrow x \geq \frac{-3}{2} \\
& \Rightarrow \frac{-3}{2} \leq x
\end{aligned}
$
and
$
\begin{aligned}
& 15-7 x>\frac{x+1}{3} \\
& \Rightarrow 45-21 x>x+1 \\
& \Rightarrow 45-1>x+21 x \\
& \Rightarrow 44>22 x \\
& 2>x \Rightarrow x=2 \\
& \therefore \frac{-3}{2} \leq x<2, x \in R
\end{aligned}
$
\begin{aligned}
& -3(x-7) \geq 15-7 x>\frac{x+1}{3}, n \in R \\
& -3(x-7) \geq 15-7 x \Rightarrow 3 x+21 \geq 15-7 x \\
& -3 x+7 x \geq 15-21 \Rightarrow 4 x \geq-6 \\
& \Rightarrow x \geq \frac{-6}{4} \\
& \Rightarrow x \geq \frac{-3}{2} \\
& \Rightarrow \frac{-3}{2} \leq x
\end{aligned}
$
and
$
\begin{aligned}
& 15-7 x>\frac{x+1}{3} \\
& \Rightarrow 45-21 x>x+1 \\
& \Rightarrow 45-1>x+21 x \\
& \Rightarrow 44>22 x \\
& 2>x \Rightarrow x=2 \\
& \therefore \frac{-3}{2} \leq x<2, x \in R
\end{aligned}
$
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