Problem 51 Solve each equation, and check y... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 2: Problem 51

Solve each equation, and check your solution. $$ 3 x+7-2 x=0 $$

Short Answer

Expert verified

x = -7

Step by step solution

Combine Like Terms

To simplify the equation, first combine the terms involving x. The equation is given as: o 3x + 7 - 2x = 0Combining the like terms, we get: o (3x - 2x) + 7 = 0This simplifies to: o x + 7 = 0

Isolate the Variable

Next, solve for x by isolating the variable. Subtract 7 from both sides: o x + 7 - 7 = 0 - 7This simplifies to: o x = -7

Check the Solution

To ensure the solution is correct, substitute x = -7 back into the original equation: o 3(-7) + 7 - 2(-7)This becomes: o -21 + 7 + 14 = 0Simplify the left side: o -21 + 21 = 0This confirms the solution is correct, as both sides of the equation are equal.

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Key Concepts

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

Combining Like Terms

When solving linear equations, one of the initial steps involves combining like terms. Like terms are terms that have the same variable raised to the same power. In the equation provided, $3x + 7 - 2x = 0$, the like terms are $3x$ and $-2x$. By combining these, we simplify the expression.
First, identify the coefficients of the $x$ terms, which are 3 and -2. Combine these by performing the necessary arithmetic operation (here, subtraction):

$3x - 2x = x$

This leaves us with the simplified equation $x + 7 = 0$. Combining like terms reduces the complexity of the equation, making it easier to handle in subsequent steps.

Isolating the Variable

After simplifying the equation, the next step is to isolate the variable. Isolating the variable means getting the variable (in this case, $x$) by itself on one side of the equation. For $x + 7 = 0$, we perform the opposite operation of addition, which is subtraction, to remove the constant term from the left side.
Subtract 7 from both sides of the equation:

$x + 7 - 7 = 0 - 7$

This simplifies to:

$x = -7$

Thus, $x = -7$ is the solution. By isolating the variable, we determine the value of $x$ that satisfies the equation.

Checking the Solution

The last step in solving linear equations is to check the solution. This ensures that the value we found for the variable is correct. To check the solution, substitute $x = -7$ back into the original equation $3x + 7 - 2x = 0$.
Replace $x$ with -7:

$3(-7) + 7 - 2(-7)$

Perform the multiplication and addition:

$-21 + 7 + 14$

Combine the terms:

$-21 + 21 = 0$

Both sides of the equation are equal, confirming that $x = -7$ is indeed the correct solution. Checking the solution helps verify that no mistakes were made during the problem-solving process.

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91影视

Solve each equation, and check your solution. $$ 3 x+7-2 x=0 $$

Short Answer

Step by step solution

Combine Like Terms

Isolate the Variable

Check the Solution

Key Concepts

Combining Like Terms

Isolating the Variable

Checking the Solution

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