Problem 37 Solve. $$ 12 \cdot x=1944 ... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 5: Problem 37

Solve. $$ 12 \cdot x=1944 $$

Short Answer

Expert verified

x = 162

Step by step solution

Understand the Equation

The equation given is a simple linear equation: $ 12 \times x = 1944 $. The goal is to solve for the variable $ x $.

Isolate the Variable

To solve for $ x $, divide both sides of the equation by the coefficient of $ x $, which is 12: $ x = \frac{1944}{12} $.

Perform the Division

Calculate the value by performing the division: $ x = 162 $.

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Key Concepts

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

linear equations

A linear equation is an equation that represents a straight line when plotted on a graph. The general form of a linear equation is $ax + b = c$, where $a$, $b$, and $c$ are constants and $x$ is the variable. Linear equations have one variable and the variable is only to the first power.
In our exercise, the equation is $12x = 1944$. Here, $a = 12$, $b = 0$, and $c = 1944$.
The goal is to find the value of $x$ that makes this equation true.
To solve it, we perform operations to isolate $x$ on one side of the equation.

arithmetic operations

Arithmetic operations are basic mathematical procedures such as addition, subtraction, multiplication, and division. In solving linear equations, we often use these operations to isolate the variable.
In our equation $12x = 1944$, we need to use division to solve for $x$.
Here's a step-by-step process:

Identify the operation needed to isolate $x$. Here, since 12 is multiplied by $x$, we'll need to divide by 12 to cancel it out.
Apply the same operation to both sides of the equation to keep it balanced. This is known as the principle of equality.

division in algebra

Division is the arithmetic operation of splitting a number into equal parts. In algebra, we use division to isolate variables and solve equations.
In our problem $12x = 1944$, to isolate $x$, we divide both sides of the equation by 12:
\[\frac{12x}{12} = \frac{1944}{12}\]\br>This simplifies to: \[ x = 162 \]Breaking it down:

First, recognize that we want to isolate $x$. The 12 attached to $x$ means multiplication.
To reverse multiplication, we use division. So, divide both sides by 12.
Carry out the division: $1944 梅 12 = 162$.

Now we know $x = 162$, which is the solution to the equation.

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91影视

Solve. $$ 12 \cdot x=1944 $$

Short Answer

Step by step solution

Understand the Equation

Isolate the Variable

Perform the Division

Key Concepts

linear equations

arithmetic operations

division in algebra

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