Problem 23 Solve the equations. Write the a... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 4: Problem 23

Solve the equations. Write the answers as fractions or whole numbers. $$6=-\frac{1}{4} x$$

Short Answer

Expert verified

The solution is $ x = -24 $.

Step by step solution

Isolate the variable

To solve the equation, isolate the variable by getting rid of the coefficient of x. In this case, the coefficient is $-\frac{1}{4}$.

Multiply both sides by the reciprocal

The reciprocal of $-\frac{1}{4}$ is $-4$. Multiply both sides of the equation by $-4$ to isolate x.\[ 6 \times (-4) = x \ 6 \times (-4) = -\frac{1}{4} x \times (-4) \ -24 = x \ x = -24 \]

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Key Concepts

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

Isolate the Variable

When solving linear equations, the first essential step is to isolate the variable you're solving for. This means you want to get the variable on one side of the equation by itself.
In the given exercise, the equation is: $6 = -\frac{1}{4} x$. Here, $x$ is the variable we want to isolate.
To isolate the variable:

Identify the coefficient (the number that multiplies the variable). In this case, it's $-\frac{1}{4}$.
Undo the multiplication by the coefficient by performing the opposite operation, which we will cover in the next steps.

By isolating the variable, you simplify the equation and set the groundwork for solving it.

Reciprocal

The next concept you need to understand is the reciprocal. The reciprocal of a number is essentially 1 divided by that number. For example, the reciprocal of $2$ is $\frac{1}{2}$ and the reciprocal of $-4$ is $-\frac{1}{4}$.
In our exercise, the coefficient of $x$ is $-\frac{1}{4}$.
To isolate $x$, we need to multiply both sides of the equation by the reciprocal of $-\frac{1}{4}$, which is $-4$.
Reciprocals are key to 'undoing' multiplication and division with fractions in equations.

Multiplication

Our final step involves multiplication. After determining that the reciprocal of $-\frac{1}{4}$ is $-4$, we multiply both sides of the original equation $6 = -\frac{1}{4} x$ by $-4$ to isolate $x$.
This gives us: \[6 \times (-4) = x\]Simplifying the multiplication, we get: \[ -24 = x \]
Thus, $x = -24$.
Multiplying by reciprocals is an effective way to isolate variables, especially when dealing with fractions. Remember to always perform the same operation on both sides of the equation to maintain equality.

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91影视

Solve the equations. Write the answers as fractions or whole numbers. $$6=-\frac{1}{4} x$$

Short Answer

Step by step solution

Isolate the variable

Multiply both sides by the reciprocal

Key Concepts

Isolate the Variable

Reciprocal

Multiplication

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