He only did the first inequality and ignored the second because he took "or"
to mean that you are to solve either the first inequality or the second
inequality, whichever you choose, and you do not need to even look at the
other one.
But that's the wrong way to take "or".
5x - 6 < -16 or -4x ≤ -20
If he's listening, the problem is to give the solution set for this:
{x | 5x-6 < -16} U {x | -4x ≤ -20}
The U means the union of the two sets.
----------------------------------------------------------------
Solve the first inequality:
5x - 6 < -16
Add +6 to both sides:
5x < -10
Divide both sides by 5, which does NOT flip the inequality, because we
are dividing by a POSITIVE.
x < -10 <--first inequality simplified
******************************************************************
Now solve the second inequality
-4x ≤ -20
Divide both sides by -4, which DOES flips the inequality, because we
are dividing by a NEGATIVE.
x ≥ 5 <--second inequality simplified
******************************************************************
We plot the first one:
x < -10 <--first inequality simplified.
Plot it on a number line by shading everything left of -10, and we put an open
circle at -10 because the inequality is < and not ≤.
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
<=========o------------------------------------------------------------------------
Now we plot the second one:
x ≥ 5 <--second inequality simplified.
Plot it on a number line by shading the 5 and everything RIGHT of 5, and we put a
closed circle at 5 because the inequality is ≥ and not >.
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
----------------------------------------------------------------------☻===========>
Now we combine the two number lines because what is shaded must be in the solution
for the first inequality OR the second inequality.
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
<=========o-----------------------------------------------------------☻===========>
Then we write the solution set in interval notation, which is an abbreviation for
the above number line:
(-∞,-10) U [5,∞) <--answer
Edwin
