Solving Inequalities with Two Absolute Values by Testing Points

This may not be an SAT/ACT inequalities question, but it's more difficult than those seen on SAT or ACT. So, if you understand the two techniques demonstrated in this video about solving inequalities, you will become a lot better on your SAT or ACT preparation!
We are solving the inequality |x+3|+|x-1| less than or equal to 8 by breaking into cases and testing points.
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[@ahmadmhmd5465]

Awesome thank you so much❤❤

[@GlassofNumbers]

Thank you! Please help me share the video with others 😁👍

[@kingsleyosei3256]

Love it ❤

[@GlassofNumbers]

Thank you! Please help me share my video as well! 👍😁

[@rnegoro1]

Nice

[@GlassofNumbers]

Thank you!

[@chloe-jw6nt]

why do we need to draw the number line if u already got x=3,=5? cant u just automatically make the link to [-5,3]

[@GlassofNumbers]

Because the solution could been (-inf, -5] or [3, inf), so we need to test points and check.

[@weneverforgetwearelegion]

does it always work?

[@GlassofNumbers]

Yeah, for this type.

[@user-kg2ro2fn2p]

If on R.H.S has > 8 then what will be the cases to solve the question

[@GlassofNumbers]

Good question! The process is similar, but we want the sum of the absolute values to be greater than 8.

[@peaceful_flow639]

If we have 0 instead of 8 and it is just |x+3| + |x-1|

[@GlassofNumbers]

Correct! In that case, we only consider the equation. And no need to test points since |x+3| and |x-1| must be both zero at the same time in order for the equation to be true. Can we get a solution then?

[@thanhloan4342]

in VIET NAM , we have x+3+x-1 = 8 and -8 . that enought

[@GlassofNumbers]

Ok!

[@user-wd5tw2eo7s]

Number line before -5 y isn't it in solution

[@moonsuyoung2407]

i love you

[@GlassofNumbers]

Thank you! Please help me share my video 😁👍

[@atineeabanga-jk4gh]

Abanga

[@GlassofNumbers]

?

[@MATHMAN-qz3de]

try and solve something like |x+1|>|x+3|

[@GlassofNumbers]

If we move |x+3| to the left side, it is similar to the question in this video.

[@user-ot1il3wl5r]

劉有吟

[@user-ot1il3wl5r]

我是她女兒 0:02

[@GlassofNumbers]

??