Answer:
A) x < 15
Explanation:
You want the solution to x/3 < 5.
Inequality
The steps to solving an inequality are basically identical to the steps for solving an equation. There are a couple of differences:
- the direction of the inequality symbol must be respected
- multiplication/division by negative numbers reverses the inequality symbol
1-step
If this were and equation, it would be a "one-step" equation. That step is to multiply both sides by the inverse of the coefficient of x.
The coefficient of x is 1/3. Its inverse is 3. Multiplying both sides by 3, we have ...
3(x/3) < 3(5)
x < 15 . . . . . . . . . simplify
Note that 3 is a positive number, so we leave the inequality symbol pointing the same direction.
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Additional comment
We can swap the sides of an equation based on the symmetric property of equality:
a = b ⇔ b = a
When we swap the sides of an inequality, we need to preserve the relationship between them. (This is the meaning of "respect the direction of the inequality symbol".)
a < b ⇔ b > a
Besides multiplying and dividing by a negative number, there are other operations that affect the order of values.
- -2 < 1 ⇔ 2 > -1 . . . . . multiply by -1
- 2 < 3 ⇔ 1/2 > 1/3 . . . . . take the reciprocal (same signs)
- a < b ⇔ cot⁻¹(a) > cot⁻¹(b) . . . . use function having negative slope
Note that the 1/x function is another one that has negative slope, which is why it reverses the ordering for values with the same sign. (It has no effect on ordering of values with opposite signs.)