The task is to find the range for x such that:
-2x+ 3
< 5
As of solving all algebraic equations and inequalities, the motivation is to
make the unknown the subject. We do so by systematically getting rid of terms which are in the
way.
First, we want to get rid of the 3 on the LHS (left hand side) by minusing
3 on both sides:
-2x+ 3 -3 < 5 -3
-2x <
2
Next, we want to get rid of the coefficient in front of the x. To be exact,
actually we are trying to reduce it to 1. We do so by dividing both sides by "-2".
But...
WARNING
As a rule
of thumb, when dealing with inequalities, when we multiply or divide by negative numbers, we have
to flip the inequality sign.
Therefore,
x>-1
To be convinced of the
solution,
Click on the link provided at the bottom of this
answer.
The expression "-2x+3" (red graph) will only be less than
"5" (blue graph) in the region when x is greater than -1
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