Answer:
[tex]-37\leq x\:<19[/tex]
Step-by-step explanation:
To find the values of [tex]x[/tex] for which, the value of [tex]\frac{3-x}{8}[/tex] belongs to [tex](-2,5][/tex],we solve the inequality;
[tex]-2\:<\frac{3-x}{8}\leq 5[/tex]
We multiply through by 8 to obtain;
[tex]-16\:<3-x\leq 40[/tex]
We subtract 3 to get
[tex]-19\:<-x\leq 37[/tex]
Divide through by -1 to obtain;
[tex]19\:>x\ge-37[/tex]
Or
[tex]-37\leq x\:<19[/tex]
The values of the x the fraction (3-x)/8 belong to the interval (−2; 5] is [tex]\rm -37\leq x<19[/tex].
Given
Fraction; [tex]\rm \dfrac{3-x}{8}[/tex] belong to the interval (−2; 5].
An interval comprises the numbers lying between two specific given numbers.
The inequality is solved for the given interval l (−2; 5] following all the steps given below.
Therefore,
The value of x is;
[tex]\rm- 2<\dfrac{3-x}{8}\leq 5\\\\\text{Multiply by 8 }\\\\8 \times -2 < 8 \times \dfrac{3-x}{8}\leq 8 \times 5\\\\ -16<3-x\leq 40\\\\\text{Subtract 3 from both sides}\\\\ -16-3<-3+3-x\leq -3+40\\\\ -19<-x\leq 37\\\\19>x\geq -37\\\\-37\leq x<19[/tex]
Hence, the values of the x the fraction (3-x)/8 belong to the interval (−2; 5] is [tex]\rm -37\leq x<19[/tex].
To know more about interval click the link is given below.
https://brainly.com/question/13048073
