Solve the compound  inequality -4 ≤ 3 + 7x ≤ 24.   Show the solution sets written algebraically and as a union or intersection of intervals. Describe in words what the solution sets mean,...

Solve the compound  inequality -4 ≤ 3 + 7x ≤ 24.

  

Show the solution sets written algebraically and as a union or intersection of intervals. Describe in words what the solution sets mean, and then display a simple line graph for the solution. 

Asked on by awlgeelady

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

`-4lt=3+7xlt=24`

To solve, we have to isolate the x at the middle.

To do so, subtract the whole equation by 3.

`-4-3<=3-3+7x<=24-3`

`-7lt=7xlt=21`

And, divide the whole equation by 7.

`(-7)/7lt=(7x)/xlt=21/7`

`-1lt=xlt=3`

Hence, the solution to the inequality equation is `-1lt=xlt=3` .

durbanville's profile pic

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

So continuing the principle from the first post with your correction now in place this renders:

-1`<=` x and x `<=` 3

Thus:

The solution set in words:

This indicates all the numbers to the right of and including -1 and all the numbers to the left of and including 3 . So the intersection is all the numbers between and including -1 and 3.

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