Question

solve the following inequality. graph the solution set and write it in interval notation.
13x < 12x + 3

choose the graph of the solution set.
a. number line with arrow to left from 3, open circle
b. number line with arrow to right from 5, closed circle
c. number line with arrow to right from 2, open circle
d. number line with arrow to left from 0, closed circle
e. number line with arrow to both sides, all real numbers?
f. empty number line?

Explanation:

Step1: Subtract \(12x\) from both sides

To solve the inequality \(13x < 12x + 3\), we subtract \(12x\) from both sides to isolate the variable \(x\).

$$13x - 12x < 12x + 3 - 12x$$

Step2: Simplify both sides

Simplifying the left side gives \(x\) and the right side gives \(3\). So the solution to the inequality is \(x < 3\).

For the graph of the solution set \(x < 3\), we need an open circle at \(3\) (since \(x\) is not equal to \(3\)) and an arrow pointing to the left (since \(x\) is less than \(3\)). Looking at the options, option A has an open circle at \(3\) and the arrow pointing to the left, which matches our solution.

Answer:

The solution to the inequality \(13x < 12x + 3\) is \(x < 3\). The interval notation is \((-\infty, 3)\). The graph of the solution set is option A.