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Chapter 2: Problem 243

Solve each linear equation. $$21+2(m-4)=25$$

Short Answer

Expert verified
m = 6

Step by step solution

01

Distribute the 2

Distribute the 2 through the parentheses. The equation becomes: \[ 21 + 2m - 8 = 25 \]
02

Combine like terms

Combine the constants on the left side of the equation: \[ 13 + 2m = 25 \]
03

Isolate the variable term

Subtract 13 from both sides to isolate the term with the variable: \[ 2m = 12 \]
04

Solve for m

Divide both sides by 2 to solve for \( m \): \[ m = 6 \]

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Key Concepts

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

Distributive Property
When you see an expression like \(2(m-4)\), you need to apply the distributive property. This property allows you to multiply a single term with each term inside the parentheses. In this case, you distribute the \(2\) to both \(m\) and \(-4\). The equation \(21 + 2(m-4)\) turns into \[21 + 2m - 8 = 25\]. This step simplifies the equation and makes it easier to solve.
Combining Like Terms
After distributing, it's crucial to combine like terms. Like terms are terms that have the same variable or none at all. In the equation \(21 + 2m - 8 = 25\), the constants \(21\) and \(-8\) are like terms because they don't have variables. Adding these constants together gives \[21 - 8 = 13\]. Now, the equation simplifies to \[13 + 2m = 25\]. Combining like terms helps in reducing the complexity of the equation.
Isolating Variables
To isolate the variable, you need to get the term containing the variable on one side of the equation by itself. In the equation \[13 + 2m = 25\], you subtract \(13\) from both sides. This action leaves the term \(2m\) alone on one side and simplifies the other side: \[25 - 13 = 12\]. This simplifies the equation to \[2m = 12\]. Isolating the variable term is essential to prepare for solving for the variable.
Solving for Variables
Finally, you solve for the variable by performing division or multiplication as needed. In the simplified equation \[2m = 12\], you divide both sides by \(2\) to find the value of \(m\). So, \[m = 12 / 2 = 6\]. This gives you the solution to the equation, which is \(m = 6\). Solving for the variable is the final step and provides the specific value that satisfies the original equation.

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