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**Breaking It Down: Simple Steps to Success**

**What’s the Puzzle?** Let’s look at the equation “5x – 12 = 0”. It might look a bit confusing at first, but don’t worry! It’s like a puzzle, and we’re going to solve it together.

**Step 1: Meet the Equation** In our equation, we have “5x – 12 = 0”. Think of ‘x’ as a mystery number we need to find. The ‘5’ is its friend that’s multiplying with it, and ‘-12’ is another number that’s just hanging out on the same side.

**Step 2: Make ‘x’ Feel Special** Our goal is to find ‘x’, so we need to make it feel special. To do this, we want to get ‘x’ alone on one side of the equation.

**Step 3: Dealing with ‘-12’** Right now, ‘-12’ is taking up space next to ‘x’. To move it, we do something cool: we add 12 to both sides of the equation. This cancels the -12. So, our equation becomes “5x – 12 + 12 = 0 + 12”, which simplifies to “5x = 12”.

**Step 4: Freeing ‘x’** Now, ‘x’ is multiplied by 5. To set it free, we do the opposite of multiplying: we divide. So, we divide both sides by 5. This gives us “5x ÷ 5 = 12 ÷ 5”. Simplifying this, we get “x = 12/5”.

**Step 5: The Mystery Solved!** After doing the math, we find that “x = 2.4”. That’s our mystery number!

Certainly! Let’s solve the equation “5x – 12 = 0” with a detailed explanation and an example.

**Solution to the Equation: 5x – 12 = 0**

**Starting Point**: The original equation is “5x – 12 = 0”.**Isolating x**: The goal is to find the value of ‘x’. To do this, we need to isolate ‘x’ on one side of the equation.**Eliminate -12**: We see that -12 is subtracted from 5x. To move it to the other side, we add 12 to both sides of the equation. This is because adding 12 cancels out the -12 on the left side. So, the equation becomes:

[ 5x – 12 + 12 = 0 + 12 ]

Simplified, it is:

[ 5x = 12 ]**Divide by 5**: ‘x’ is currently being multiplied by 5. To get ‘x’ alone, we divide the entire equation by 5. This is because dividing by 5 cancels out the multiplication by 5. The equation is now:

[ \frac{5x}{5} = \frac{12}{5} ]

Simplified, it is:

[ x = \frac{12}{5} ]**Simplified Result**: Finally, simplifying the fraction 12/5, we find that:

[ x = 2.4 ]

So, the solution to the equation “5x – 12 = 0” is ( x = 2.4 ).

**Solved Equation Example**

Let’s use an example to see how this solution works in a real-world scenario.

**Scenario**: Imagine you have 5 bags, and each bag can hold a certain number of apples. However, you are 12 apples short of filling all the bags completely. If you fill each bag completely, how many apples are in each bag?

**Representing the Scenario**: Let the number of apples that each bag can hold be ‘x’. The total number of apples required to fill all 5 bags is ‘5x’. Being 12 apples short is represented as ‘-12’.**Equation**: The equation representing this scenario is:

[ 5x – 12 = 0 ]**Solving**: Following the steps above, we find that:

[ x = 2.4 ]**Interpreting the Result**: Each bag can hold 2.4 apples. Since you can’t have a fraction of an apple in real life, this might mean that the scenario requires a little adjustment, like maybe some bags have 2 apples and others have 3.

This example demonstrates how algebra can be applied to understand and solve real-world problems.

**Congratulations!**

You’ve just solved the equation “5x – 12 = 0” and found that ‘x’ equals 2.4. Great job! Remember, equations are just puzzles waiting to be solved, and now you have the skills to tackle them.