Problem 64 Solve each equation, and check y... [FREE SOLUTION]

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Chapter 2: Problem 64

Solve each equation, and check your solution. $$ 4(k-6)-(3 k+2)=-5 $$

Short Answer

Expert verified

k = 21

Step by step solution

- Distribute and simplify

Distribute the 4 into the parentheses: 4(k - 6) - (3k + 2) = -5=> 4k - 24 - 3k - 2 = -5.

- Combine like terms

Combine like terms: 4k - 3k - 24 - 2 = -5=> k - 26 = -5.

- Solve for k

Add 26 to both sides to isolate the variable k: k - 26 + 26 = -5 + 26=> k = 21.

- Check the solution

Substitute k = 21 back into the original equation to verify: 4(21 - 6) - (3(21) + 2) = -5=> 4 * 15 - (63 + 2) = -5=> 60 - 65 = -5=> -5 = -5.

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Key Concepts

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

Distribution in Algebra

The first step in our problem involves distributing a number across terms inside parentheses.
Here, we have the expression $4(k - 6) - (3k + 2) = -5$.
We use distribution to multiply 4 by each term inside its parentheses. This results in $4 \times k - 4 \times 6$.
The expression then becomes: $4k - 24$. We also have \-(3k + 2), which changes both the signs inside the parentheses:
$-3k - 2$.
So, the equation simplifies to $4k - 24 - 3k - 2 = -5$.

Combining Like Terms

After distribution, we look to combine like terms - terms that have the same variables or constant values.
In $4k - 24 - 3k - 2$, we see $4k$ and $-3k$ as like terms because they both have the variable k.
So, $4k - 3k$ simplifies to $k$.
We also have the constants $-24$ and $-2$, which simplify to $-26$.
This gives us the simplified equation: $k - 26 = -5$.
Combining like terms helps to simplify and make the equation more solvable.

Isolating Variables

Next, we want to isolate the variable $k$. This means getting $k$ alone on one side of the equation.
The current equation is $k - 26 = -5$.
To isolate $k$, we need to undo the subtraction by adding $26$ to both sides of the equation. This gives us:
$k - 26 + 26 = -5 + 26$.
Simplifying both sides gives $k = 21$.
Now, $k$ is isolated, and we have found that $k = 21$ solves the equation.

Checking Solutions in Algebra

Lastly, it's important to check if our solution is correct by substituting $k = 21$ back into the original equation.
The original equation is $4(k - 6) - (3k + 2) = -5$.
Substituting $21$ into the equation, we get:
$4(21 - 6) - (3(21) + 2)$.
First, solve inside the parentheses:
$4 \times 15 - (63 + 2) = -5$.
This results in $60 - 65 = -5$, which simplifies to $-5 = -5$.
Since both sides of the equation are equal, our solution is verified to be correct!

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91影视

Solve each equation, and check your solution. $$ 4(k-6)-(3 k+2)=-5 $$

Short Answer

Step by step solution

- Distribute and simplify

- Combine like terms

- Solve for k

- Check the solution

Key Concepts

Distribution in Algebra

Combining Like Terms

Isolating Variables

Checking Solutions in Algebra

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