Problem 204 Solve the following equations wi... [FREE SOLUTION]

Chapter 2: Problem 204

Solve the following equations with variables and constants on both sides. $$4 a+5=-a-40$$

Short Answer

Expert verified

$a = -9$

Step by step solution

Combine Like Terms

To start solving the equation, move the variable terms to one side. Add 'a' to both sides of $4a + 5 = -a - 40$. This simplifies to $5a + 5 = -40$.

Isolate the Variable Term

Move the constant term to the other side of the equation. Subtract 5 from both sides: $5a + 5 - 5 = -40 - 5$. This simplifies to $5a = -45$.

Solve for the Variable

Divide both sides by 5 to isolate 'a': $\frac{5a}{5} = \frac{-45}{5}$. Simplifying this, we get $a = -9$.

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Key Concepts

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

combining like terms

Combining like terms is a crucial step in solving linear equations. Like terms are terms that contain the same variable raised to the same power. When you have an equation with terms on both sides, you should first aim to collect all the variable terms on one side.
In the example equation, $4a + 5 = -a - 40$, we start by adding 'a' to both sides:
\[ 4a + 5 + a = -a + a - 40 \]
This simplifies to:
\[ 5a + 5 = -40 \]
Here, we have successfully combined the like terms, gathering all 'a' terms on one side of the equation.

isolating the variable

The next step is to isolate the variable term. Isolating the variable makes it easier to solve for the variable. This involves moving constants to the opposite side of the equation.
In our current equation, we have:\[ 5a + 5 = -40 \]
To isolate the variable term ($5a$), we need to remove the constant term (+5) from the left side. We do this by subtracting 5 from both sides of the equation:
\[ 5a + 5 - 5 = -40 - 5 \]
This results in:
\[ 5a = -45 \]
Now, the variable term $5a$ is isolated on the left side, making it easier to solve for 'a'.

solving for variables

After isolating the variable term, the final step is to actually solve for the variable. This usually involves basic arithmetic, such as division or multiplication.
In our equation, we are left with:
\[ 5a = -45 \]
To solve for 'a', we need to get 'a' by itself. This means dividing both sides by 5, the coefficient of 'a':
\[ \frac{5a}{5} = \frac{-45}{5} \]
Which simplifies to:
\[ a = -9 \]
So, the solution to the equation is $a = -9$. By following these clear steps鈥攃ombining like terms, isolating the variable, and solving for the variable鈥攜ou can solve linear equations more easily.

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91影视

Solve the following equations with variables and constants on both sides. $$4 a+5=-a-40$$

Short Answer

Step by step solution

Combine Like Terms

Isolate the Variable Term

Solve for the Variable

Key Concepts

combining like terms

isolating the variable

solving for variables

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