Problem 45 Solve and check. $$12=3+w$$... [FREE SOLUTION]

Chapter 5: Problem 45

Solve and check. $$12=3+w$$

Short Answer

Expert verified

The solution to the given equation is $w = 9$.

Step by step solution

Isolate the variable

In order to solve for 'w', one needs to isolate it on one side of the equation. This can be achieved by subtracting '3' from both sides of the equation. This allows the equation: $12 - 3 = 3 + w - 3$

Simplify the equation

After carrying out the subtraction on both sides, the equation simplifies to: $9 = w$

Verification

To check if $9$ is the correct value for 'w', it can be substituted back into the original equation. This gives: $12 = 3 + 9$, which after simplifying becomes $12 = 12$. This initially verifies that $9$ is indeed the correct value for 'w'.

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Key Concepts

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

Isolate the Variable

The first step in solving a linear equation is to isolate the variable, meaning to get the variable by itself on one side of the equation. For example, in the equation 12=3+w, the goal is to find the value of w. To isolate w, subtract 3 from both sides of the equation to effectively remove it from the side containing the variable:

12 - 3 = w + 3 - 3

Notice that subtracting 3 from the side with w cancels out the addition of 3, leaving w by itself. The process of isolating the variable often involves performing the inverse operation to whatever is being done to the variable.

Simplifying Equations

Once we've begun to isolate the variable, simplifying the equation is a crucial step. Simplifying makes the equation easier to understand and solve. In our example, after subtracting 3 from both sides, we get a simpler form: 9 = w. This clearly shows what w equals, without any additional numbers or operations complicating the equation. Simplifying can involve combining like terms, distributing multiplications over additions or subtractions, and reducing fractions to their simplest form. The key is to perform the same operation on both sides of the equation to maintain balance.

Equation Verification

Lastly, verification is an essential part in solving equations. After we think we have solved for the variable, we must check to ensure our solution is correct. We do this by substituting the solved value back into the original equation. From our previous step, we believe that w = 9, so we replace w with 9 in the original equation:

12 = 3 + 9

After simplifying, we get 12 = 12, which confirms our solution since both sides of the equation are equal. This process helps catch any mistakes and solidifies the understanding that our solution is indeed valid for the given equation.

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91影视

Solve and check. $$12=3+w$$

Short Answer

Step by step solution

Isolate the variable

Simplify the equation

Verification

Key Concepts

Isolate the Variable

Simplifying Equations

Equation Verification

One App. One Place for Learning.

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