Problem 515 In the following exercises, solv... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 4: Problem 515

In the following exercises, solve. $$7 k=18$$

Short Answer

Expert verified

k = \frac{18}{7}

Step by step solution

Identify the Equation

The given equation is: \[ 7k = 18 \] This is a linear equation where k is the variable to solve for.

Isolate the Variable

To isolate the variable on one side of the equation, divide both sides of the equation by the coefficient of k (which is 7): \[ k = \frac{18}{7} \]

Simplify the Answer

Simplify the fraction to get the final answer: \[ k = \frac{18}{7} \] The fraction is already in its simplest form.

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Key Concepts

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

linear equations

Linear equations are fundamental in algebra. They involve variables, typically represented by letters like x, y, or in our case, k. The beauty of linear equations is their simplicity. They are easy to identify and manipulate.
A linear equation takes the form: \[ ax + b = c \] where 'a', 'b', and 'c' are constants. In the given exercise, the equation is \[ 7k = 18 \] Here, 'k' is our variable, and 7 and 18 are constants.
The goal is to find the value of 'k' that makes the equation true.

isolating variables

Isolating the variable means getting the variable by itself on one side of the equation. This is done by performing operations that will 'undo' whatever is attached to the variable.
In the exercise, we have: \[ 7k = 18 \] We need to isolate 'k'. The equation tells us that 7 times 'k' equals 18. To detach 'k' from the 7, we divide both sides of the equation by 7:

\[ k = \frac{18}{7} \] Dividing by 7 'cancels out' the multiplication on the left side, leaving 'k' isolated.

simplifying fractions

Simplifying fractions can make your final answer easier to understand and more useful. A fraction is in simplest form when the numerator (top number) and the denominator (bottom number) have no common factors other than 1.
In our example, after isolating 'k', we have: \[ k = \frac{18}{7} \]

This fraction is already in its simplest form because there are no numbers other than 1 that can divide both 18 and 7. Simplifying fractions usually involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that number.
Understanding this makes it easier to handle fractions in algebra and other areas of math.

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91影视

In the following exercises, solve. $$7 k=18$$

Short Answer

Step by step solution

Identify the Equation

Isolate the Variable

Simplify the Answer

Key Concepts

linear equations

isolating variables

simplifying fractions

One App. One Place for Learning.

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