Question

Solve the inequality 2v/5 < 2 and write the solution in interval notation.

a. v < 5
b. v > 5
c. v < 10
d. v > 10

Answer 1

The inequality 2v/5 < 2 is solved by multiplying both sides by 5 and then dividing by 2, resulting in v < 5. In interval notation, the solution is (-∞, 5). Option (a) is the correct answer.

Step-by-step explanation:

To solve the inequality 2v/5 < 2, we need to isolate the variable v. We do this by performing the same operations on both sides of the inequality.

1. Multiply both sides by 5 to eliminate the denominator on the left side: 5 * (2v/5) < 5 * 2, which simplifies to 2v < 10.
2. Now, divide both sides by 2 to solve for v: 2v/2 < 10/2, resulting in v < 5.

In interval notation, this inequality is expressed as (-∞, 5).

Therefore, the correct answer is v < 5, which corresponds to option (a).