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To solve for \( x \) when \( h(x) = -8 \) given the function \( h(x) = 5x + 2 \), we can set up the equation:

\[
5x + 2 = -8
\]

Subtract 2 from both sides:

\[
5x = -10
\]

Divide both sides by 5:

\[
x = -2
\]

So, the value of \( x \) when \( h(x) = -8 \) is \( x = -2 \).

Would you like to go through any steps in more detail or do you have any other questions on this topic? Here are some related questions you might consider:

1. How would the solution change if the equation was \( h(x) = 5x - 2 \) instead?
2. What is the graphical interpretation of finding \( x \) when \( h(x) = -8 \)?
3. How would you solve the equation if \( h(x) \) involved a quadratic term, such as \( h(x) = 5x^2 + 2 \)?
4. Can you explain how to check if \( x = -2 \) is indeed the correct solution?
5. What happens to the value of \( h(x) \) as \( x \) increases or decreases?

Tip: Always verify your solution by substituting it back into the original equation to ensure it satisfies the equation.

Given h(x) = 5x + 2, solve for x when h(x) = -8.

Learn how to solve the linear equation h(x) = 5x + 2 for h(x) = -8 with a detailed step-by-step explanation. This problem demonstrates key algebraic concepts suitable for students in Grades 6-8.

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