Problem 50 The product of $-3.6$ and a nu... [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 5: Problem 50

The product of $-3.6$ and a number is 48.3 more than the number. Find the number.

Short Answer

Expert verified

The number is approximately -10.5.

Step by step solution

Set up the equation

Let the unknown number be represented by the variable $ x $. According to the exercise, the product of $ -3.6 $ and $ x $ is equal to $ 48.3 $ more than the number. This can be written as the equation: \[ -3.6x = x + 48.3 \]

Combine like terms

To solve for $ x $, first move all terms involving $ x $ to one side of the equation. Start by subtracting $ x $ from both sides: \[ -3.6x - x = 48.3 \] Combine the $ x $ terms on the left side: \[ -4.6x = 48.3 \]

Solve for x

To isolate $ x $, divide both sides of the equation by $ -4.6 $: \[ x = \frac{48.3}{-4.6} \] Calculate the value: \[ x \approx -10.5 \]

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Key Concepts

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

equation setup

To solve the problem, we first need to translate the text into a mathematical form. Let's denote the unknown number by the variable $ x $. The problem states that the product of $ -3.6 $ and the unknown number is 48.3 more than the unknown number. Hence, we write the equation as:
\[ -3.6x = x + 48.3 \]
Here, the left side represents the product of $ -3.6 $ and the number ($ x $), and the right side represents 48.3 more than the number ($ x $). This equation effectively sets up the problem for solving.

combining like terms

Next, we need to simplify the equation by combining like terms. Our current equation is:
\[ -3.6x = x + 48.3 \]
To combine like terms, we need to get all the $ x $ terms on one side of the equation. Subtracting $ x $ from both sides, we get:
\[ -3.6x - x = 48.3 \]
This simplifies to:
\[ -4.6x = 48.3 \]
Combining like terms helps simplify the equation and makes it easier to solve in the next steps.

isolating the variable

Isolating the variable is crucial to find its value. From the combined equation:
\[ -4.6x = 48.3 \]
we need to get $ x $ alone. The term $ -4.6x $ implies that $ x $ is multiplied by $ -4.6 $. To isolate $ x $, divide both sides of the equation by $ -4.6 $:
\[ x = \frac{48.3}{-4.6} \]
This division cancels out the $ -4.6 $ on the left, leaving $ x $ by itself. Isolating the variable sets the stage for the final calculation.

solving for x

Finally, solving for $ x $ involves computing the result of the isolated equation:
\[ x = \frac{48.3}{-4.6} \]
When we divide $ 48.3 $ by $ -4.6 $, we get approximately:
\[ x \approx -10.5 \]
Therefore, the unknown number is approximately $ -10.5 $.
This brings us to the end of the problem by finding the value of the unknown number.

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91影视

The product of \(-3.6\) and a number is 48.3 more than the number. Find the number.

Short Answer

Step by step solution

Set up the equation

Combine like terms

Solve for x

Key Concepts

equation setup

combining like terms

isolating the variable

solving for x

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