July 24, 2024

Solving the Equation: 5x – 12 = 0

Contents

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

  1. Starting Point: The original equation is “5x – 12 = 0”.
  2. 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.
  3. 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 ]
  4. 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} ]
  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?

  1. 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’.
  2. Equation: The equation representing this scenario is:
    [ 5x – 12 = 0 ]
  3. Solving: Following the steps above, we find that:
    [ x = 2.4 ]
  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.

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