Problem 47 Solve each equation, and check y... [FREE SOLUTION]

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Chapter 2: Problem 47

Solve each equation, and check your solution. $$ 1.2 y-4=0.2 y-4 $$

Short Answer

Expert verified

y = 0

Step by step solution

- Move variable terms to one side

Subtract 0.2y from both sides: 1.2y - 0.2y - 4 = -4.

- Simplify the equation

Combine like terms on the left-hand side: 1.0y - 4 = -4.

- Isolate the variable

Add 4 to both sides to isolate y: 1.0y - 4 + 4 = -4 + 4. Therefore, y = 0.

- Check the solution

Substitute y = 0 back into the original equation to verify: 1.2(0) - 4 = 0.2(0) - 4. This simplifies to -4 = -4, which is true. Thus, y = 0 is the correct solution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Variable Isolation

To solve any linear equation, the first step is to isolate the variable. This means that you want to get the unknown variable, in this case, y, by itself on one side of the equation. In our example, we start with the equation: $1.2y - 4 = 0.2y - 4$ To isolate y, you need to remove the terms involving y from one side. This is achieved by subtracting $0.2y$ from both sides:$1.2y - 0.2y - 4 = -4$By doing so, we gather all of the y terms on one side of the equation. Remember, whatever you do to one side of the equation, you must do to the other side as well. This keeps the equation balanced.

Simplifying Equations

After isolating the variable on one side, the next step is simplifying the equation. We'll combine the like terms to make the equation easier to solve. Combining $1.2y - 0.2y$ simplifies to $1.0y$. So, our equation becomes: $1.0y - 4 = -4$Simplifying equations often involves combining terms and clearing out constants. In this case, the constant -4 is already present on both sides, making the equation straightforward to solve. Simplifying helps us see the solution more clearly and reduces the complexity.

Checking Solutions

Once you have isolated the variable and simplified the equation, the final step is to check your solution. This is crucial in verifying that the solution is correct. You do this by substituting the value back into the original equation. In our case, we calculated that $y = 0$. Substituting $y = 0$ back into the original equation we get:$1.2 \times 0 - 4 = 0.2 \times 0 - 4$This simplifies to $-4 = -4$, which confirms our solution is correct. Always checking your solution ensures that no mistakes were made in your calculations. It is an essential step in solving linear equations effectively.

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91影视

Solve each equation, and check your solution. $$ 1.2 y-4=0.2 y-4 $$

Short Answer

Step by step solution

- Move variable terms to one side

- Simplify the equation

- Isolate the variable

- Check the solution

Key Concepts

Variable Isolation

Simplifying Equations

Checking Solutions

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