Solve |x| = 5: Finding Solutions to an Absolute Value Equation

To solve the equation $\left| x \right| = 5$, consider what absolute value means. The absolute value $\left| x \right|$ represents the distance between $x$ and 0 on the number line, meaning it’s always non-negative.

When solving $\left| x \right| = 5$, we find the values of $x$ that are 5 units away from 0. Hence, the absolute value equation $\left| x \right| = 5$ results in two possible equations:

• $x = 5$
• $x = -5$

So, the solutions to the absolute value equation $\left| x \right| = 5$ are $x = 5$ and $x = -5$.

Let's compare these solutions to the answer choices provided:

• Choice 1: $x = 5$ matches one solution.
• Choice 2: $x = -5$ matches the other solution.
• Choice 4: "Answers a + b" suggests both are correct, which is indeed the case.

Thus, the choice that correctly represents the solutions to the equation $\left| x \right| = 5$ is "Answers a + b".

Therefore, the correct answer is:

Answers a + b