https://file.aiquickdraw.com/mathbot/file/1728539484278rp1asod7.jpg

The equation shown in the image is:

\[
15x - 2 = 85 - 4(x - 2)
\]

Let's solve for \( x \).

### Step 1: Simplify the right-hand side
First, distribute the \(-4\) on the right-hand side:

\[
15x - 2 = 85 - 4(x - 2)
\]
\[
15x - 2 = 85 - 4x + 8
\]
\[
15x - 2 = 93 - 4x
\]

### Step 2: Move all \( x \)-terms to one side
Add \(4x\) to both sides to get rid of the \( -4x \) on the right:

\[
15x + 4x - 2 = 93
\]
\[
19x - 2 = 93
\]

### Step 3: Isolate \( x \)
Add 2 to both sides to get:

\[
19x = 95
\]

### Step 4: Solve for \( x \)
Finally, divide both sides by 19:

\[
x = \frac{95}{19} = 5
\]

Thus, the solution is \( x = 5 \).

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

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Here are 5 related questions to consider:
1. How would the steps change if the equation involved fractions?
2. What happens if you have two variables in the equation instead of one?
3. Can you solve a system of equations using this method?
4. How do you solve quadratic equations that are not linear like this one?
5. How does this equation relate to solving inequalities?

**Tip:** Always combine like terms and simplify both sides of the equation before isolating the variable!

Solve the equation: 15x - 2 = 85 - 4(x - 2).

Learn how to solve the linear equation 15x - 2 = 85 - 4(x - 2) with a detailed step-by-step explanation. Understand algebraic techniques such as using the distributive property and isolating variables. Suitable for students in Grades 7-10.

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