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Solve the inequality 2x - 5 <= -x +12. Give your answer as an interval.
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Your starting inequality is
2x - 5 <= -x + 12.
Add "x" to both sides. You will get an equivalent inequality
2x + x - 5 <= -x + x + 12, or
3x - 5 <= 12.
Add 5 to both sides. You will get an equivalent inequality
3x - 5 + 5 <= 12 + 5, or
3x <= 17.
Now divide both sides by 3. You will get an equivalent inequality
x <= .
It is the solution set. In the interval form, it is (,]. ANSWER
Solved.
The standard solution procedure is collecting the terms with the unknown
in one side of the inequality and collecting constant terms in the other side;
then combining the like terms in each side and expressing the unknown variable in form of inequality.