Solve the following equation and then check your solution. Show all of your work.

Question

24-3x=-27

Answer 1

To solve the equation \( 24 - 3x = -27 \), we will follow these steps:

1. Isolate the term with \( x \): Start by subtracting 24 from both sides of the equation:

   \[ 24 - 3x - 24 = -27 - 24 \]

   Simplifying both sides gives:

   \[ -3x = -51 \]

2. Solve for \( x \): Next, divide both sides by -3:

   \[ x = \frac{-51}{-3} \]

   Simplifying this division gives:

   \[ x = 17 \]

Now that we have \( x = 17 \), we'll check the solution by substituting \( x \) back into the original equation:

Checking the solution:

Substituting \( x = 17 \) into the left side of the equation:

\[ 24 - 3(17) \]

Calculating \( 3(17) \):

\[ 3(17) = 51 \]

Now substituting this back into the equation:

\[ 24 - 51 = -27 \]

The left side simplifies to:

\[ -27 = -27 \]

Since both sides of the equation are equal, our solution is confirmed to be correct.

Thus, the solution to the equation \( 24 - 3x = -27 \) is

\[ \boxed{17} \]

Answer 2

can you make it less advanced

Answer 3

Sure! Let's go through the steps to solve the equation \( 24 - 3x = -27 \) in a simpler way.

Step 1: Start with the Original Equation

We have:

\[ 24 - 3x = -27 \]

Step 2: Move 24 to the Right Side

To get the term with \( x \) by itself, we need to get rid of the 24 on the left side. We can do this by subtracting 24 from both sides of the equation.

\[ 24 - 3x - 24 = -27 - 24 \]

This simplifies to:

\[ -3x = -51 \]

Step 3: Solve for \( x \)

Now we want to get \( x \) by itself. Since we have \(-3x\), we can divide both sides by -3:

\[ x = \frac{-51}{-3} \]

When we divide, the negatives cancel out:

\[ x = 17 \]

Step 4: Check the Solution

Now, let's check if our answer is correct by plugging \( x = 17 \) back into the original equation.

Substitute \( 17 \) for \( x \):

\[ 24 - 3(17) \]

First, calculate \( 3(17) \):

\[ 3(17) = 51 \]

Now substitute that into the equation:

\[ 24 - 51 \]

This gives us:

\[ -27 \]

Since the left side of the equation (which is \(-27\)) is equal to the right side (which is \(-27\)), our solution is correct!

Final Answer

So, the value of \( x \) is:

\[ \boxed{17} \]