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Chapter 3: Problem 75

\(y+4=0\)

Short Answer

Expert verified
y = -4

Step by step solution

01

Isolate the Variable

Start by isolating the variable, which in this case is y. To do that, subtract 4 from both sides of the equation.
02

Perform the Subtraction

Subtract 4 from both sides: \[ y + 4 - 4 = 0 - 4 \]
03

Simplify

Simplify the equation to find the value of y: \[ y = -4 \]

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Key Concepts

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

isolating the variable
To solve a linear equation, the first important step is isolating the variable. In simple terms, this means getting the variable alone on one side of the equation. Our goal is to find the value of the variable that makes the equation true. Let's use the example equation from the problem: \[ y + 4 = 0 \]In this equation, the variable to isolate is \( y \). Think of it like peeling an onion: you need to remove the layers around \( y \) to see its value clearly. In this case, we have to remove the `+ 4` term that's keeping \( y \) from being by itself. Remember, whatever we do to one side of the equation, we must do to the other side too. This helps keep the equation balanced.
subtraction property of equality
The subtraction property of equality states that if you subtract the same number from both sides of an equation, the equation remains equal. It's like a see-saw, where both sides must stay balanced. Let's look at our example equation again: \[ y + 4 = 0 \] To remove `+ 4` and isolate \( y \), subtract 4 from both sides: \[ y + 4 - 4 = 0 - 4 \]Perform the subtraction: \[ y = -4 \]By subtracting 4 from both sides, we've used the subtraction property of equality to keep the equation balanced while isolating the variable. Great job! Now \( y \) is all by itself, and its value is more clear.
simplifying equations
Simplifying equations is a crucial step in solving them. In our example, after we applied the subtraction property of equality, we needed to tidy up the equation: \[ y + 4 - 4 = 0 - 4 \]Subtracting `4` from `4` cancels out the `4` on the left, simplifying it to just \( y \). On the right-hand side, 0 minus 4 simplifies to \[ y = -4 \]Simplifying helps to make the equation neater and clearly shows the value of the variable. When the equation is simplified, it is easier to see that \( y = -4 \). This means simplifying is the final touch on solving the equation, making everything clear and straightforward.

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Most popular questions from this chapter

Graph each linear equation. $$ y=-\frac{3}{4} x+3 $$

Write an equation of the line satisfying the given conditions. Give the final answer in slope-intercept form. (Hint: Recall the relationships among slopes of parallel and perpendicular lines.) Parallel to \(5 x-y=10\) \(y\) -intercept (0,-2)

$$ y=-\frac{1}{2} x+2 $$

$$ y=\frac{7}{3} x-6 $$

$$ (-4,4), \text { slope } 0 $$
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