Josefina Started To Solve For X X X In The Equation 3.5 = 1.9 − 0.8 ∣ 2 X − 0.6 ∣ 3.5=1.9-0.8|2x-0.6| 3.5 = 1.9 − 0.8∣2 X − 0.6∣ Using The Steps Below:1. $3.5=1.9-0.8|2x-0.6|$2. $1.6=-0.8|2x-0.6|$3. − 2 = ∣ 2 X − 0.6 ∣ -2=|2x-0.6| − 2 = ∣2 X − 0.6∣ Why Did Josefina Stop At Step 3?

Josefina is attempting to solve for $x$ in the equation $3.5=1.9-0.8|2x-0.6|$. To do this, she follows a series of steps to isolate the variable $x$. However, she stops at Step 3, and in this article, we will explore why she did so.

Step 1: Initial Equation

The initial equation is $3.5=1.9-0.8|2x-0.6|$. This equation involves an absolute value, which means that the expression inside the absolute value can be either positive or negative.

3.5 = 1.9 - 0.8|2x - 0.6|

Step 2: Isolating the Absolute Value

Josefina's next step is to isolate the absolute value by subtracting 1.9 from both sides of the equation. This gives her the equation $1.6=-0.8|2x-0.6|$.

1.6 = -0.8|2x - 0.6|

Step 3: Removing the Absolute Value

Josefina then removes the absolute value by multiplying both sides of the equation by -1/0.8. This gives her the equation $-2=|2x-0.6|$.

-2 = |2x - 0.6|

Why Josefina Stopped at Step 3

Josefina stopped at Step 3 because she realized that she had reached an impasse. The equation $-2=|2x-0.6|$ is a two-case equation, meaning that it has two possible solutions. The absolute value can be either positive or negative, which means that the expression inside the absolute value can be either $2x-0.6=2$ or $2x-0.6=-2$.

2x - 0.6 = 2 \quad \text{or} \quad 2x - 0.6 = -2

However, Josefina realized that she had not yet isolated the variable $x$, and that she needed to take further steps to solve for $x$. She could have continued by solving each case separately, but she chose to stop at Step 3.

Solving the Two-Case Equation

To solve the two-case equation, we need to consider each case separately.

Case 1: $2x-0.6=2$

2x - 0.6 = 2

Solving for $x$, we get:

2x = 2.6
x = 1.3

Case 2: $2x-0.6=-2$

2x - 0.6 = -2

Solving for $x$, we get:

2x = -1.4
x = -0.7

Conclusion

In conclusion, Josefina stopped at Step 3 because she realized that she had reached an impasse. She had not yet isolated the variable $x$, and she needed to take further steps to solve for $x$. By considering each case separately, we can solve the two-case equation and find the values of $x$.

Key Takeaways

• When solving an equation with an absolute value, we need to consider each case separately.
• The two-case equation can be solved by considering each case separately.
• By following the steps outlined in this article, we can solve the equation $3.5=1.9-0.8|2x-0.6|$ and find the values of $x$.
  Q&A: Understanding the Equation and Josefina's Steps =====================================================

In our previous article, we explored the equation $3.5=1.9-0.8|2x-0.6|$ and followed the steps that Josefina took to isolate the variable $x$. However, she stopped at Step 3, and in this article, we will answer some frequently asked questions about the equation and Josefina's steps.

Q: Why did Josefina stop at Step 3?

A: Josefina stopped at Step 3 because she realized that she had reached an impasse. She had not yet isolated the variable $x$, and she needed to take further steps to solve for $x$.

Q: What is the two-case equation?

A: The two-case equation is an equation that has two possible solutions. In this case, the absolute value can be either positive or negative, which means that the expression inside the absolute value can be either $2x-0.6=2$ or $2x-0.6=-2$.

Q: How do I solve the two-case equation?

A: To solve the two-case equation, you need to consider each case separately. In this case, we solved the two-case equation by considering each case separately and finding the values of $x$.

Q: What are the values of $x$?

A: The values of $x$ are $1.3$ and $-0.7$. These values were found by solving the two-case equation and considering each case separately.

Q: Why is it important to isolate the variable $x$?

A: It is important to isolate the variable $x$ because it allows us to solve for the value of $x$. In this case, we were able to find the values of $x$ by isolating the variable $x$ and solving the two-case equation.

Q: What are some common mistakes to avoid when solving equations with absolute values?

A: Some common mistakes to avoid when solving equations with absolute values include:

• Not considering each case separately
• Not isolating the variable $x$
• Not solving the two-case equation

Q: How can I practice solving equations with absolute values?

A: You can practice solving equations with absolute values by working through examples and exercises. You can also try solving equations with absolute values on your own and checking your answers with a calculator or a friend.

Q: What are some real-world applications of solving equations with absolute values?

A: Solving equations with absolute values has many real-world applications, including:

• Physics: Solving equations with absolute values is used to model real-world phenomena such as motion and energy.
• Engineering: Solving equations with absolute values is used to design and optimize systems such as bridges and buildings.
• Economics: Solving equations with absolute values is used to model real-world phenomena such as supply and demand.

Conclusion

In conclusion, solving equations with absolute values requires careful consideration of each case separately and isolation of the variable $x$. By following the steps outlined in this article, you can solve the equation $3.5=1.9-0.8|2x-0.6|$ and find the values of $x$. Remember to practice solving equations with absolute values and to avoid common mistakes such as not considering each case separately and not isolating the variable $x$.