Problem 29 Solve each equation, and check y... [FREE SOLUTION]

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Chapter 2: Problem 29

Solve each equation, and check your solution. $$ 3 x=2 x+7 $$

Short Answer

Expert verified

The solution is $x = 7$.

Step by step solution

- Move all x terms to one side

Start by subtracting $2x$ from both sides of the equation: \[3x - 2x = 2x + 7 - 2x\] This simplifies to: \[x = 7\]

- Verify the solution

Substitute $x = 7$ back into the original equation to verify: \[3(7) = 2(7) + 7\] Calculating both sides we get: \[21 = 14 + 7\] Since both sides are equal, $x = 7$ is indeed a solution.

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Key Concepts

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

Equation Solving

Solving linear equations is a vital skill in algebra. It involves finding the value of the variable that makes the equation true. In our example, we have the equation $3x = 2x + 7$. The goal is to isolate the variable, which in this case is $x$.
We start by moving all terms involving $x$ to one side. By subtracting $2x$ from both sides, we get: \[3x - 2x = 2x + 7 - 2x\] This simplifies to: \[x = 7\]
This process of moving terms helps us ensure the variable $x$ is by itself on one side of the equation, making it easier to find its value.

Verification of Solutions

After finding a potential solution, verifying it ensures it is indeed correct. Verification involves substituting the found value back into the original equation.
For our solution $x = 7$, we substitute it back into the original equation: \[3(7) = 2(7) + 7\] This simplifies to: \[21 = 14 + 7\] Both sides of the equation are equal, confirming our solution is correct.
Verification is an important step as it helps confirm there was no error in the solving process. By seeing that both sides of the equation match, we ensure the reliability of our solution.

Algebraic Manipulation

Algebraic manipulation involves using the rules of algebra to simplify or rearrange equations to make solving easier. Here, subtraction was used to isolate the variable.
The process involves these simple steps:

Identify like terms.
Move terms involving the variable to one side.
Combine like terms to simplify.

In our equation $3x = 2x + 7$, we subtracted $2x$ from both sides to get: \[3x - 2x = x\] Having isolated $x$, we easily saw that \[x = 7\]
Mastering these manipulations makes solving more complex equations straightforward.

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91影视

Solve each equation, and check your solution. $$ 3 x=2 x+7 $$

Short Answer

Step by step solution

- Move all x terms to one side

- Verify the solution

Key Concepts

Equation Solving

Verification of Solutions

Algebraic Manipulation

One App. One Place for Learning.

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