Respuesta :

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The easiest way to solve this is as an inequality. Here's what it's saying we have:
[tex]-2 \leq {\frac{5-2b}{4}}\leq1[/tex]

First, multiply everything by 4 to clear the denominator:
[tex]-8\leq5-2b\leq4[/tex]

Subtract 5 from both sides:
[tex]-13\leq-2b\leq-1[/tex]

In the last step, we need to divide everything by -2 which will flip both inequality signs, so we have:
[tex]\frac{13}{2}\geq b \geq \frac{1}{2}[/tex]

So b is in the interval [tex][\frac{1}{2},\frac{13}{2}][/tex].

Answer:  The required value of b lies in the interval [0.5, 6.5].

Step-by-step explanation:  We are given to find the value of b so that the following fraction belong to the interval [−2, 1] :

[tex]f=\dfrac{5-2b}{4}.[/tex]

According to the given information, we can write

[tex]-2\leq f\leq 1\\\\\Rightarrow -2\leq \dfrac{5-2b}{4}\leq1\\\\\Rightarrow -8\leq 5-2b\leq 4\\\\\Rightarrow -8-5\leq-2b\leq 4-5\\\\\Rightarrow -13\leq -2b\leq -1\\\\\Rightarrow 13\geq 2b\geq 1\\\\\Rightarrow \dfrac{13}{2}\geq b\geq \dfrac{1}{2}\\\\\Rightarrow 6.5\geq b\geq 0.50[/tex]

Thus, the required value of b lies in the interval [0.5, 6.5].

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