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Please help me with this:
5x-7 < 2x+5
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They want you solve this inequality
5x - 7 < 2x + 5.
Apply a standard procedure solving linear inequality.
Add 7 to both sides of the inequality. You will get an equivalent inequality
5x - 7 + 7 < 2x + 5 + 7.
Combine like terms in both sides
5x < 2x + 12.
Now subtract 2x from both sides. You will get an equivalent inequality
5x - 2x < 2x + 12 - 2x.
Combine like terms in both sides
3x < 12.
Divide both sides by 3. You will get an equivalent inequality
x < 4.
This last inequality determines the solution set, which is all rel numbers that are less than 4.
ANSWER. The solution set is {x < 4}, i.e. all real numbers that are less than 4.
In the interval form, the solution is (,).
Solved.
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The standard solution procedure of solving such inequalities 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.
If you want to see other examples on solving similar inequalities, look into the lesson
- Solving simple and simplest linear inequalities
in this site.
Learn the subject from there.