Given h, of, x, equals, 4, x, minus, 5*h*(*x*)=4*x*−5, solve for x*x* when h, of, x, equals, 7*h*(*x*)=7.

To solve the problem, we start with the function definition and the condition provided:

Given the function:
\[
h(x) = 4x - 5
\]

and the condition:
\[
h(x) = 7
\]

we need to solve for \(x\).

### Step 1: Set up the equation using the given condition

Substitute \(h(x) = 7\) into the function:
\[
4x - 5 = 7
\]

### Step 2: Solve the equation for \(x\)

1. Add 5 to both sides of the equation:
   \[
   4x = 7 + 5
   \]

2. Simplify the right side:
   \[
   4x = 12
   \]

3. Divide both sides by 4:
   \[
   x = \frac{12}{4}
   \]

4. Simplify:
   \[
   x = 3
   \]

### Final Answer

\[
x = 3
\]

Would you like more details on any step, or do you have any questions?

Here are some related questions you might find interesting:

1. How do you solve similar equations with different constants?
2. What happens if the function is modified to \( h(x) = ax - b \) with arbitrary \(a\) and \(b\)?
3. How would you graph the function \( h(x) = 4x - 5 \)?
4. Can \(h(x)\) be defined differently, such as with a quadratic term?
5. How would you verify the solution graphically?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the given condition!

Given h(x) = 4x - 5, solve for x when h(x) = 7.

Learn how to solve the linear equation h(x) = 4x - 5 by setting it equal to 7 and finding the value of x. This tutorial is ideal for students in Grades 6-8 and covers essential algebraic techniques.

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