Problem 38 Solve each equation, and check y... [FREE SOLUTION]

Chapter 2: Problem 38

Solve each equation, and check your solution. $$ -6 x+3=-7 x+10 $$

Short Answer

Expert verified

The solution is x = 7. Verifying this value satisfies the original equation.

Step by step solution

- Combine Like Terms

First, add 7x to both sides of the equation to combine like terms. -6x + 7x + 3 = -7x + 7x + 10 This simplifies to: x + 3 = 10

- Isolate the Variable Term

Next, subtract 3 from both sides to isolate the variable x. x + 3 - 3 = 10 - 3 This simplifies to: x = 7

- Check the Solution

Substitute x = 7 back into the original equation to check the solution. -6(7) + 3 = -7(7) + 10 This simplifies to: -42 + 3 = -49 + 10 Which simplifies further to: -39 = -39 Since both sides of the equation are equal, x = 7 is the correct solution.

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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 first steps is to combine like terms. Like terms are terms that contain the same variable raised to the same power. This makes it easier to simplify the equation.

In the equation given: $-6x + 3 = -7x + 10$, we have variables on both sides. In order to combine like terms, we want to get all the $x$-terms on one side of the equation.

We do this by adding $7x$ to both sides:
$-6x + 7x + 3 = -7x + 7x + 10$.

This simplifies to a simpler form: $x + 3 = 10$.

By combining like terms, the equation is easier to solve because similar terms have been grouped together, thus reducing the complexity of the problem.

Isolating the Variable

Next comes isolating the variable. This means getting the variable $x$ all by itself on one side of the equation, so we can easily determine its value.

From the previous step, we simplified our equation to $x + 3 = 10$.
To isolate $x$, we need to remove the constant term on the same side as $x$.

Since $3$ is being added to $x$, we subtract $3$ from both sides to keep the equation balanced:
$x + 3 - 3 = 10 - 3$.

This simplifies to $x = 7$.

Now, the variable $x$ is isolated, and its value is $7$. Isolating the variable makes it clear what $x$ equals, which is the goal of solving the equation.

Checking the Solution

After finding the value of the variable, it's important to check the solution to ensure it satisfies the original equation.

To do this, substitute $x = 7$ back into the original equation: $-6x + 3 = -7x + 10$.

Replace $x$ with $7$:
$-6(7) + 3$ should equal $-7(7) + 10$.

Calculate both sides: $-42 + 3 = -49 + 10$.

Simplify further: $-39 = -39$.

Since both sides of the equation are equal, our solution $x = 7$ is verified to be correct.

Checking the solution ensures there are no mistakes and confirms that the equation holds true with the value found for the variable.

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91影视

Solve each equation, and check your solution. $$ -6 x+3=-7 x+10 $$

Short Answer

Step by step solution

- Combine Like Terms

- Isolate the Variable Term

- Check the Solution

Key Concepts

Combining Like Terms

Isolating the Variable

Checking the Solution

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