Problem 22 Solve each equation, and check y... [FREE SOLUTION]

Chapter 2: Problem 22

Solve each equation, and check your solution. $$ -7=x-22 $$

Short Answer

Expert verified

x = 15

Step by step solution

- Isolate the variable

Begin by isolating the variable ( x ) on one side of the equation. To do this, add 22 to both sides of the equation: -7 + 22 = x - 22 + 22d

- Simplify both sides

Next, simplify both sides. The equation becomes 15 = x.

- Write the final solution

The final solution is x = 15.

- Check the solution

Substitute x with 15 in the original equation to verify: -7 = 15 - 22 . Simplifying the right-hand side, we get -7 = -7 . Since both sides are equal, the solution is verified.

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Key Concepts

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

Isolate the Variable

To solve a linear equation, one of the main objectives is to isolate the variable on one side of the equation. This means adjusting the equation so that the variable you are solving for is on its own. For instance, consider the equation:

$-7 = x - 22$

If you start with the equation above, you want to get 鈥榎(x\)鈥� by itself on one side. You can do this by performing operations that eliminate other numbers from the side with the variable. These operations must keep the two sides of the equation equal. For this particular problem, you need to add 22 to both sides:

$-7 + 22 = x - 22 + 22$

This step essentially cancels out the 22 on the right side, leaving 鈥榎(x\)鈥� isolated.

Understanding this step is crucial as isolating the variable helps you find the value of that variable.

Simplifying Equations

Once the variable is isolated, the next step is to simplify both sides of the equation. Simplification makes the equation easier to solve and understand. In our example:

We've isolated the variable to get the equation:

$-7 + 22 = x$

Now, you perform the arithmetic on the numbers:

$15 = x$

In other words, the equation simplifies to show the value of $x$. Simplifying equations helps in verifying that the operations done are correct and that the equation balances out.

Checking Solutions

After solving for the variable, it's pivotal to check that your solution is correct. This is done by substituting the variable back into the original equation. For the current example, we found:

$x = 15$

We substitute $15$ back to the original equation:

$-7 = 15 - 22$

Simplify the right-hand side:

$-7 = -7$

If both sides of the equation are equal after substitution, the solution is verified as correct. This final check ensures no mistakes were made and that the solution makes sense within the context of the original problem.

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91影视

Solve each equation, and check your solution. $$ -7=x-22 $$

Short Answer

Step by step solution

- Isolate the variable

- Simplify both sides

- Write the final solution

- Check the solution

Key Concepts

Isolate the Variable

Simplifying Equations

Checking Solutions

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