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Chapter 2: Problem 145

Translate to an equation and then solve. -152 is the product of 8 and \(q\).

Short Answer

Expert verified
The value of \(q\) is -19.

Step by step solution

01

Understand the Problem

Read the problem carefully. It states that -152 is the product of 8 and a variable, which we will call \(q\). This means we need to set up an equation where -152 equals 8 times \(q\).
02

Set Up the Equation

From the problem statement, we can write the equation: \(-152 = 8 \cdot q\).
03

Isolate the Variable

To solve for \(q\), divide both sides of the equation by 8: \(\frac{-152}{8} = q\).
04

Simplify the Division

Perform the division: \(-152 \div 8 = -19\). Hence, \(q = -19\).

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Key Concepts

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

Algebraic Equations
Algebraic equations are mathematical statements that show the equality between two expressions. In this exercise, we have to translate a statement into an algebraic equation. The given statement is '-152 is the product of 8 and q'.
To set up the algebraic equation, we identify that the product of 8 and the variable, represented by q, equals -152. Hence, we write: \[-152 = 8 \times q\]. This equation tells us that if you multiply 8 by some number q, you get -152.
Solving algebraic equations often involves understanding relationships between numbers and variables. We'll be using different operations, like multiplication or division, to find the value of the variable.
Isolating Variables
Isolating variables is a key step in solving algebraic equations. It means getting the variable by itself on one side of the equation. This helps us see the solution to the problem clearly. In our equation \[-152 = 8 \times q\], we need to find the value of q. To do this, we want to have q alone on one side.
We achieve isolation by performing operations that undo what has been done to the variable. Here, q is being multiplied by 8. To isolate q, we need to perform the opposite operation, which is division. Therefore, we divide both sides of the equation by 8: \[\frac{-152}{8} = q\]. This step ensures that q is now by itself.
Basic Arithmetic Division
Basic arithmetic division is an essential operation in math. It splits a number into equal parts. In our exercise, we need to divide -152 by 8 to isolate q. This is how we find the unknown variable's value.
Here's how the division works:
-152 divided by 8 can be shown as \[-152 \div 8\]. When we perform this division, it results in -19. Hence, \q = -19\. This step confirms our solution.
Remember, dividing a negative number by a positive one results in a negative outcome. Division is straightforward if you follow the steps methodically.

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