Solve the following equation. Then identify the equation as an​ identity, an inconsistent​ equation, or a conditional equation.

4​(x−4​)=4x−16

To solve the equation \(4(x - 4) = 4x - 16\), we will first simplify both sides and then determine the type of equation.

### Step 1: Expand and simplify both sides
Start by expanding the left side:

\[
4(x - 4) = 4x - 16
\]

Distribute the 4:

\[
4x - 16 = 4x - 16
\]

### Step 2: Analyze the equation
Now, observe that both sides of the equation are identical:

\[
4x - 16 = 4x - 16
\]

Since both sides are the same, the equation holds true for **all values of \(x\)**.

### Step 3: Identify the type of equation

Since the equation is true for all values of \(x\), it is classified as an **identity**.

### Conclusion

The equation \(4(x - 4) = 4x - 16\) is an **identity** because it is true for all values of \(x\).

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Would you like more details on this process, or do you have any other questions?

Here are some related questions you might consider:
1. What is the difference between an identity and a conditional equation?
2. How do you determine if an equation is inconsistent?
3. Can you provide an example of a conditional equation?
4. How do you solve equations with variables on both sides?
5. What does it mean for an equation to have no solution?

**Tip:** When solving equations, always simplify both sides first to see if the equation reduces to a simpler form.

Learn how to solve the equation 4(x - 4) = 4x - 16 step-by-step. Understand the concept of equation types: identity, inconsistent, or conditional. Suitable for students in Grades 7-9.

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