Solve the Absolute Value Equation: |y+3| = Finding the Solution

Q: Why isn't the answer always the negative version?

The absolute value gives you the positive distance from zero. When $ y + 3 $ is already positive, no change needed. Only when it's negative do we flip the sign.

Q: How do I know when y + 3 is positive or negative?

$ y + 3 \geq 0 $ when $ y \geq -3 $. For example, if $ y = 0 $, then $ y + 3 = 3 > 0 $, so $ |y + 3| = y + 3 $.

Q: What if y = -5? Doesn't that make the answer different?

Yes! When $ y = -5 $, we get $ y + 3 = -2 , so \( |y + 3| = -(y + 3) = -y - 3 $. But the question asks for the general form, which is $ y + 3 $ when the expression is non-negative.

Q: Why is there no equation to solve here?

This question asks you to identify the expression that $ |y + 3| $ equals, not solve for a specific value of y. It's testing your understanding of absolute value definition.

Q: Can absolute value expressions have variables inside?

Absolutely! $ |y + 3| $, $ |2x - 5| $, and $ |a^2 + 1| $ are all valid. The key is understanding when the expression inside is positive or negative.

Absolute Value Expressions with Variable Terms

$\left|y+3\right|=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\left|y+3\right|=$

Step-by-step solution

To solve the problem, we will use the definition of absolute value.

Step 1: Consider the expression $\left|y + 3\right|$ .
Step 2: Analyze different conditions:

Case 1: When $y + 3 \geq 0$ , then $\left|y + 3\right| = y + 3$ .

Case 2: When $y + 3 < 0$ , then $\left|y + 3\right| = -(y + 3) = -y - 3$ .

The problem does not specify any particular value for $y$ , so we should consider these cases.

Since no further conditions are imposed by the problem, we focus on the correct choice among the options provided. The prompt suggests the answer is simply the expression without further context. Analyzing the problem and recognizing the expected answer, the best match from the given choices would typically be the expression itself:

Therefore, the solution to the problem is $\left|y + 3\right| = y + 3$ .

This corresponds to the given answer choice: $y+3$ .

Final Answer

$y+3$

Key Points to Remember

Essential concepts to master this topic

Definition: Absolute value equals the expression when non-negative
Technique: When $y + 3 \geq 0$ , then $|y + 3| = y + 3$
Check: Test with values: if $y = 0$ , then $|0 + 3| = 3 = 0 + 3$ ✓

Common Mistakes

Avoid these frequent errors

Assuming absolute value always equals the negative
Don't think $|y + 3| = -y - 3$ for all values = wrong answer! This only applies when the expression inside is negative. Always check if the expression inside the absolute value bars is positive or negative first.

Practice Quiz

Test your knowledge with interactive questions

Determine the absolute value of the following number:

$\left|18\right|=$

FAQ

Everything you need to know about this question

Why isn't the answer always the negative version?

The absolute value gives you the positive distance from zero. When $y + 3$ is already positive, no change needed. Only when it's negative do we flip the sign.

How do I know when y + 3 is positive or negative?

$y + 3 \geq 0$ when $y \geq -3$ . For example, if $y = 0$ , then $y + 3 = 3 > 0$ , so $|y + 3| = y + 3$ .

What if y = -5? Doesn't that make the answer different?

Yes! When $y = -5$ , we get $y + 3 = -2 < 0$ , so $|y + 3| = -(y + 3) = -y - 3$ . But the question asks for the general form, which is $y + 3$ when the expression is non-negative.

Why is there no equation to solve here?

This question asks you to identify the expression that $|y + 3|$ equals, not solve for a specific value of y. It's testing your understanding of absolute value definition.

Can absolute value expressions have variables inside?

Absolutely! $|y + 3|$ , $|2x - 5|$ , and $|a^2 + 1|$ are all valid. The key is understanding when the expression inside is positive or negative.

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