Certainly! To solve the inequality [tex]\(5x - 25 < -15\)[/tex], we can follow a step-by-step algebraic approach:
1. Isolate the term with the variable:
We start by eliminating the constant term on the left side. We do this by adding 25 to both sides of the inequality:
[tex]\[
5x - 25 + 25 < -15 + 25
\][/tex]
This simplifies to:
[tex]\[
5x < 10
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Next, we need to get [tex]\(x\)[/tex] by itself. Since [tex]\(5x\)[/tex] means 5 times [tex]\(x\)[/tex], we divide both sides of the inequality by 5:
[tex]\[
\frac{5x}{5} < \frac{10}{5}
\][/tex]
This simplifies to:
[tex]\[
x < 2
\][/tex]
3. Interpret the solution:
The inequality [tex]\(x < 2\)[/tex] means that [tex]\(x\)[/tex] can be any number less than 2.
4. Represent the solution on a number line:
On a number line, we represent [tex]\(x < 2\)[/tex] by shading all the numbers to the left of 2. We use an open circle at 2 to indicate that 2 is not included in the solution.
Given these steps, the number line showing the solution [tex]\(x < 2\)[/tex] will have an open circle at 2 and be shaded to the left of 2.
To identify the correct number line from the given choices (A, B, C, D), look for the one where all numbers less than 2 are shaded and there is an open circle at 2.
Answer:
The correct number line is the one with an open circle at 2 and shading to the left of 2.
