Problem 8 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 8

Solve each equation, and check your solution. $$ x-18=22 $$

Short Answer

Expert verified

x = 40

Step by step solution

- Isolate the Variable

To solve for the variable $ x $, you need to isolate it on one side of the equation. Since the equation is $ x - 18 = 22 $, add 18 to both sides of the equation to cancel out the -18 on the left side.

- Perform the Operation

Add 18 to both sides of the equation: \[ x - 18 + 18 = 22 + 18 \] Simplify the equation: \[ x = 40 \]

- Check the Solution

To ensure the solution is correct, substitute $ x = 40 $ back into the original equation: \[ 40 - 18 = 22 \] Simplify the left side: \[ 22 = 22 \] Since the equation holds true, the solution is correct.

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Key Concepts

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

Isolate the variable

In any linear equation, the goal is to solve for the unknown variable. In this example, the equation is: \ x - 18 = 22 To isolate the variable, you need to get $ x $ by itself on one side of the equation. You do this by performing the opposite operation. Here, since $ x $ is being subtracted by 18, you will add 18 to both sides to cancel it out. \[ x - 18 + 18 = 22 + 18 \] By adding 18 to both sides, the -18 and +18 on the left side cancel each other out, leaving: \ x = 40 Now we have isolated the variable $ x $.

Perform arithmetic operations

After isolating the variable, the next step is to perform the necessary arithmetic operations to simplify the equation. In our example, we added 18 to both sides of the initial equation: \[ x - 18 + 18 = 22 + 18 \] Simplifying both sides, we get: \[ x = 40 \] This means the variable $ x $ equals 40. It is crucial to perform the same operation on both sides of the equation to maintain equality. This process helps balance the equation and leads to a correct solution.

Check solution

Once you have a potential solution, the final step is to check your work to ensure it's correct. You do this by substituting the value back into the original equation. For our example, substitute $ x = 40 $ into: \[ x - 18 = 22 \] Replace $ x $ with 40: \[ 40 - 18 = 22 \] Simplifying the left side, we see: \[ 22 = 22 \] The equation holds true, which confirms that $ x = 40 $ is the correct solution. Always check your solution to verify accuracy, as it ensures that no mistakes were made during the process.

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91影视

Solve each equation, and check your solution. $$ x-18=22 $$

Short Answer

Step by step solution

- Isolate the Variable

- Perform the Operation

- Check the Solution

Key Concepts

Isolate the variable

Perform arithmetic operations

Check solution

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