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Algebra
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solve 1/2 abs(10-2x)< or = 1
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\[\frac12|10-2x|\le1\]
Multiply both sides by 2 first
So that would be \[\left| 10-2x \right| \le 2\] right?
Yep
Note that |y|<x means that -x<y<x
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Now do the same to the question
is it \[\left| x \le9/2 or x \ge11/2 \right|\]?
nope, please do it step by step
\[\left| -11/2 orx \ge-9/2 \right|\]
nope don't guess and do it step by step
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The answer can't help you learn
I can just tell you the answer is 4<x<6 but you won't learn if you don't know why
how did you get that?
Again, can you do it step by step
\[\frac12|10-2x|\le1\]\[|10-2x|\le2\]\[-2\le10-2x\le2\]\[2\ge2x-10\ge-2\]\[12\ge2x\ge8\]\[6\ge x\ge4\]
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