 If h(x) = 3x+5and h(a)= 27 then what is the value of a?

Given the function \( h(x) = 3x + 5 \) and the information \( h(a) = 27 \), we can substitute \( a \) for \( x \) in the function and set it equal to 27:

\[
h(a) = 3a + 5 = 27
\]

Now, solve for \( a \):

1. Subtract 5 from both sides:
   \[
   3a = 27 - 5 = 22
   \]

2. Divide both sides by 3:
   \[
   a = \frac{22}{3}
   \]

So, the value of \( a \) is \( \frac{22}{3} \).

Would you like further details or explanations on this?

Here are 5 related questions to expand this topic:
1. How do you solve similar linear equations with different constants?
2. What if \( h(x) \) was a quadratic function, how would the process change?
3. Can you find the inverse of the function \( h(x) = 3x + 5 \)?
4. How does the slope affect the function \( h(x) = 3x + 5 \)?
5. What happens if the equation has more than one variable?

**Tip:** Always isolate the variable you are solving for by performing inverse operations systematically.

If h(x) = 3x + 5 and h(a) = 27, then what is the value of a?

Find the value of a in the linear equation h(x) = 3x + 5, where h(a) = 27. This step-by-step guide covers key algebraic concepts for students in Grades 6-8, including solving linear equations and isolating variables.

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