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.
To solve what is shown above, we get all the x terms to one side while everything else is to the other side.
When we divide both sides by a positive number, it does not flip the inequality sign.
x < 4 in interval notation is (-infinity, 4)
You can think of x < 4 as -infinity < x < 4
Replace the word "infinity" with the symbol if needed.
The graph of x < 4 on a number line has an open hole at 4 and shading to the left.
This is to visually represent all numbers smaller than 4.
The open hole means "exclude this endpoint from the solution set".
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