Problem 14 Solve each equation, and check y... [FREE SOLUTION]

Chapter 2: Problem 14

Solve each equation, and check your solution. $$ x+47=26 $$

Short Answer

Expert verified

x = -21

Step by step solution

- Isolate the Variable

Subtract 47 from both sides of the equation to isolate the variable x: \[ x + 47 - 47 = 26 - 47 \] Which simplifies to: \[ x = 26 - 47 \]

- Perform the Calculation

Calculate the right-hand side of the equation: \[ 26 - 47 = -21 \] So, the solution is: \[ x = -21 \]

- Check the Solution

Substitute $ x = -21 $ back into the original equation to verify: \[ -21 + 47 = 26 \] Since $ 26 = 26 $ is true, the solution $ x = -21 $ is correct.

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Key Concepts

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

Isolating Variables

To solve a linear equation, we first need to isolate the variable we're solving for. This means we want the variable, usually noted as x, to be on one side of the equation by itself.

Let's look at the equation from the example: x + 47 = 26.
Here, x is mixed with 47.
To isolate x, we do the opposite of adding 47, which is subtracting 47. We perform this subtraction on both sides of the equation to keep it balanced, like this: x + 47 - 47 = 26 - 47.

By doing this, we cancel out the 47 on the left side, making it just x: x = 26 - 47.
This step is crucial because it sets up the next phase where we simplify the right-hand side of the equation.

Performing Arithmetic Operations

Now that the variable x is isolated, we need to perform arithmetic operations to simplify the equation.

From the previous step, we have:
x = 26 - 47.

The next step is to perform the subtraction: 26 - 47.

When we subtract 47 from 26, we get: -21.

Therefore, we find: x = -21.

This step involves basic arithmetic but is crucial to solving the equation correctly. Always take care to perform these operations carefully to avoid mistakes.

Verifying Solutions

After solving for the variable, it's very important to check our solution. Verifying the solution ensures that no mistakes were made during the isolation and arithmetic steps.

The original equation we started with is:
x + 47 = 26.

Now, substitute the value we found for x, which is -21 back into the original equation: -21 + 47 = 26.

Perform the addition:
-21 + 47. This equals 26, which matches the right side of the equation.

Since both sides of the equation are equal, our solution x = -21 is verified as correct.

This final check is a critical step in solving any equation to ensure that the solution makes the original equation true.

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91影视

Solve each equation, and check your solution. $$ x+47=26 $$

Short Answer

Step by step solution

- Isolate the Variable

- Perform the Calculation

- Check the Solution

Key Concepts

Isolating Variables

Performing Arithmetic Operations

Verifying Solutions

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