Problem 24 Solve each linear equation. Show... [FREE SOLUTION]

Chapter 2: Problem 24

Solve each linear equation. Show your work and check your answer. $$-5 x+4=-9-4 x$$

Short Answer

Expert verified

The solution is x = 13.

Step by step solution

- Isolate variable terms on one side

Start by moving all terms containing the variable x to one side of the equation. Add 4x to both sides: -5x + 4 + 4x = -9 - 4x + 4x Simplify the expression: -1x + 4 = -9

- Isolate constant term

Subtract 4 from both sides to isolate the term containing x: -1x + 4 - 4 = -9 - 4 Simplify the expression: -1x = -13

- Solve for x

Divide both sides by -1 to solve for x: $-\frac{-1x}{-1} = \frac{-13}{-1}$ Simplify the expression: $ x = 13 $

- Check your answer

Substitute x = 13 back into the original equation to verify the solution: -5(13) + 4 = -9 - 4(13) Simplify both sides: -65 + 4 = -9 - 52 -61 = -61 Both sides are equal, so the solution is correct.

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Key Concepts

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

Isolating Variable Terms

Whenever you encounter a linear equation like $-5x + 4 = -9 - 4x$, the first step is to isolate the variable terms on one side. This means we want to collect all the x terms together.
Start by adding 4x to both sides. Why? Because this will cancel out the $-4x$ on the right side. Here's how it looks:

$-5x + 4 + 4x = -9 - 4x + 4x$
When we simplify this, we get:

$-1x + 4 = -9$
Now, all the x terms are on one side of the equation (left side).
This makes it easier to solve for x in the upcoming steps.

Solving for x

Now that the x terms are isolated, our next goal is to solve for x. To do this, we need to isolate x even further by getting rid of any constants on the same side.
Currently, we have:

$-1x + 4 = -9$
We subtract 4 from both sides to get rid of the 4 on the left side:

$-1x + 4 - 4 = -9 - 4$
Once simplified, this becomes:

$-1x = -13$
The last step to solve for x is to divide both sides by -1:

$\frac{-1x}{-1} = \frac{-13}{-1}$
This simplifies to:

$x = 13$
So, the solution to the equation is $\textbf{x = 13}$.

Verifying Solutions

Solving the equation is not the final step; verification is crucial. This ensures that our solution is correct.
Here鈥檚 how we do it. We need to substitute $x = 13$ back into the original equation:

$-5(13) + 4 = -9 - 4(13)$
Now, let鈥檚 simplify both sides:

Left side: \-65 + 4 = -61\
Right side: \-9 - 52 = -61\
Both sides simplify to $-61$, which means they are equal.
This confirms that our solution $x = 13$ is correct.
Verification is essential as it builds confidence that our solution is both correct and complete.

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91影视

Solve each linear equation. Show your work and check your answer. $$-5 x+4=-9-4 x$$

Short Answer

Step by step solution

- Isolate variable terms on one side

- Isolate constant term

- Solve for x

- Check your answer

Key Concepts

Isolating Variable Terms

Solving for x

Verifying Solutions

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