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Chapter 8: Problem 125

Solve the equation for the variable. $$9 k=8 k-11$$

Short Answer

Expert verified
k = -11

Step by step solution

01

Move Variables to One Side

Subtract \(8k\) from both sides of the equation:\[ 9k - 8k = 8k - 8k - 11 \]This simplifies to:\[ k = -11 \]

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Key Concepts

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

Prealgebra
Prealgebra forms the foundation for understanding algebra. It includes basicArithmetic, introductory Algebra, and Geometry. A fundamental skill in prealgebra is solving equations.
Linear equations like the one given here are basic but crucial. These equations help in understanding how algebra links to real-world problems.
When solving such problems, the goal is to simplify and isolate the variable. This often means doing the same operation to both sides of the equation. For example, adding, subtracting, multiplying, or dividing both sides by the same number.
In this case, the equation is: \[9k = 8k - 11\]. Our first step is to move all terms with a variable (k) to one side.
Variable Isolation
Variable isolation means getting the variable (in this case, k) alone on one side of the equation. This makes it easier to see what the variable equals. Here's how it's done in this problem.
We start with:\[9k = 8k - 11\]. To isolate k, we need to get rid of the term on the right side.
We achieve this by subtracting \(8k\) from both sides. This action is based on the principle that anything you do to one side of the equation must be done to the other. This keeps the equation balanced:
\[9k - 8k = 8k - 8k - 11\]This simplifies to:\[k = -11\].
\(k\) is now isolated and we have our solution.
Simple Equations
Simple equations can usually be solved in one or two steps. They involve basic operations like addition, subtraction, multiplication, and division.
Our example is a simple equation because it only required one step鈥攖he subtraction of \(8k\). Here鈥檚 another example of a simple equation:\[7x + 5 = 12\].
First, subtract 5 from both sides:
\[7x = 7\].
Then divide by 7:
\[x = 1\].
By practicing such problems, we build a strong math foundation. This will make more complex equations, like quadratic or polynomial equations, easier to handle in the future.

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Most popular questions from this chapter

In the following exercises, solve each equation. $$ 10 y=-5 y+60 $$

In the following exercises, solve each equation by clearing the decimals. $$ 0.6 p-1.9=0.78 p+1.7 $$

In the following exercises, solve each equation by clearing the fractions. $$ \frac{3}{4} a-\frac{1}{3}=\frac{1}{2} a+\frac{5}{6} $$

In the following exercises, solve each equation. $$ \frac{2}{3} x=6 $$

In the following exercises, solve each equation by clearing the decimals. $$ 0.8 x-0.3=0.7 x+0.2 $$
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