https://file.aiquickdraw.com/mathbot/file/1727359773154nzlioryp.jpg

The image shows the following algebraic equation:

\[
8x - 27x + 23 = 17x - 42
\]

Let's solve this step-by-step.

### Step 1: Combine like terms on both sides of the equation.
- On the left side, combine \( 8x \) and \( -27x \):

\[
8x - 27x = -19x
\]

So the equation becomes:

\[
-19x + 23 = 17x - 42
\]

### Step 2: Move the \( x \)-terms to one side of the equation.
- Subtract \( 17x \) from both sides:

\[
-19x - 17x + 23 = -42
\]

This simplifies to:

\[
-36x + 23 = -42
\]

### Step 3: Move the constants to the other side.
- Subtract 23 from both sides:

\[
-36x = -42 - 23
\]

This simplifies to:

\[
-36x = -65
\]

### Step 4: Solve for \( x \).
- Divide both sides by \( -36 \):

\[
x = \frac{-65}{-36} = \frac{65}{36}
\]

So, the solution is:

\[
x = \frac{65}{36}
\]

Would you like further details or have any questions about this solution? Here are some related problems for practice:

1. Solve: \( 5x - 3 = 12x + 8 \)
2. Solve: \( 4x - 9x + 18 = 3x - 7 \)
3. Simplify and solve: \( 6x + 2x - 5 = 8x - 12 \)
4. Solve: \( 9x - 27 = 5x + 33 \)
5. Solve for \( x \): \( 2(x + 4) = 3x - 5 \)

**Tip:** When solving equations, always aim to combine like terms and move the variable to one side before isolating it.

Solve the algebraic equation: 8x - 27x + 23 = 17x - 42

Learn how to solve the linear equation 8x - 27x + 23 = 17x - 42 through a detailed step-by-step process. This solution covers key algebraic concepts such as combining like terms and isolating variables, making it ideal for students in Grades 8-10.

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