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Chapter 2: Problem 33

Solve each equation, and check the solution. $$ 4 r=0 $$

Short Answer

Expert verified
The solution is \( r = 0 \).

Step by step solution

01

Isolate the Variable

The given equation is \( 4r = 0 \). To solve for the variable \( r \), divide both sides of the equation by 4.
02

Solve for r

Perform the division: \( \frac{4r}{4} = \frac{0}{4} \). Simplifying both sides gives \( r = 0 \).
03

Check the Solution

Substitute \( r = 0 \) back into the original equation: \( 4r = 4(0) = 0 \). Since the left side equals the right side, the solution \( r = 0 \) is correct.

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Key Concepts

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

Isolating the Variable
When solving linear equations, the first key step is isolating the variable. This means we want to get the variable, in this case, 'r', by itself on one side of the equation. For the equation \( 4r = 0 \), we need to remove the coefficient (the number multiplying the variable). By isolating 'r', we can find its value. To do this, we use operations that simplify the equation while keeping it balanced. Remember, whatever operation you perform on one side of the equation, you must do the same to the other side.
Division Properties of Equality
One useful property in algebra involves division properties of equality. This means that if you divide both sides of an equation by the same non-zero number, the equality remains true. In the equation \( 4r = 0 \), you divide both sides by 4 to simplify the equation. The equation becomes \( \frac{4r}{4} = \frac{0}{4} \), which simplifies to \( r = 0 \). This step ensures that 'r' is now isolated. Dividing both sides by the same number does not change the equality; it only simplifies the equation and brings us closer to the solution.
Solution Verification
Once you have a possible solution, it's important to verify it. To verify the solution for \( r \), substitute the value back into the original equation. For \( r = 0 \), substitute to get \( 4(0) \). This simplifies to \( 0 \), which equals the right-hand side of the original equation, confirming that \( r = 0 \) is indeed the correct solution. Verification helps ensure that your solution is accurate and that no mistakes were made during the solving process.

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