Problem 8 Solve each equation, and check y... [FREE SOLUTION]

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Chapter 2: Problem 8

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

Short Answer

Expert verified

x = 40

Step by step solution

Add 18 to Both Sides

To isolate the variable x, add 18 to both sides of the equation. This gives us: $ x - 18 + 18 = 22 + 18 $

Simplify the Equation

Simplify the left side and the right side of the equation: $ x = 40 $

Verify the Solution

To ensure that the solution is correct, substitute $ x = 40 $ back into the original equation: $ 40 - 18 = 22 $ Since both sides of the equation 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.

Additive Inverse

When solving linear equations, one useful technique is using the additive inverse. The additive inverse of a number is what you add to a number to get zero. For example, the additive inverse of -18 is 18 because -18 + 18 equals 0.
In the exercise, the equation is: \[ x - 18 = 22 \]
To solve for x, we need to eliminate the -18 from the left side. We do this by adding its additive inverse, which is 18:
\[ x - 18 + 18 = 22 + 18 \]
The -18 and 18 cancel each other out on the left side, leaving us with:
\[ x = 40 \] This technique of using the additive inverse helps in the isolation of the variable.

Isolation of Variables

Isolating the variable is crucial in solving linear equations. Isolation means to get the variable by itself on one side of the equation.
In our exercise, the original equation is:
\[ x - 18 = 22 \]
Our goal is to isolate x. We start by using the additive inverse of -18, which is 18, to both sides of the equation. This gives us:
\[ x - 18 + 18 = 22 + 18 \]
After simplifying, we have:
\[ x = 40 \] At this point, we have successfully isolated the variable x. This method helps in simplifying and solving equations systematically.

Verification of Solutions

After isolating the variable and solving the equation, it's essential to verify the solution. Verification ensures that the value of the variable satisfies the original equation.
In our exercise, we found that x = 40. To verify, substitute 40 back into the original equation:
\[ x - 18 = 22 \]
Substituting x with 40 gives us:
\[ 40 - 18 = 22 \]
Simplifying the left side, we see that:
\[ 22 = 22 \] Since both sides are equal, our solution x = 40 is verified. Verification helps confirm the accuracy of our solution.

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91影视

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

Short Answer

Step by step solution

Add 18 to Both Sides

Simplify the Equation

Verify the Solution

Key Concepts

Additive Inverse

Isolation of Variables

Verification of Solutions

One App. One Place for Learning.

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