Problem 117 Solve the equation for the varia... [FREE SOLUTION]

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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 8: Problem 117

Solve the equation for the variable. $$4 m+9=-23$$

Short Answer

Expert verified

m = -8

Step by step solution

Isolate the Variable Term

Subtract 9 from both sides of the equation to isolate the term with the variable on one side. $4m + 9 - 9 = -23 - 9 $ $ 4m = -32 $

Solve for the Variable

Divide both sides of the equation by 4 to solve for $m$. $ \frac{4m}{4} = \frac{-32}{4} $ $m = -8$

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Key Concepts

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

Isolating the Variable

To solve any linear equation, the main goal is to isolate the variable. This means getting the variable on one side of the equation by itself. For instance, in our example equation, we have:
$4m + 9 = -23$
The aim is to rearrange the equation so that $m$ is by itself on one side. We do this because it makes it clear what value the variable holds. When the variable is isolated, it's much easier to see the solution to the equation. Isolating the variable often involves a few steps, such as adding, subtracting, multiplying, or dividing both sides of the equation.

Subtracting from Both Sides

One of the most common techniques to isolate the variable is subtracting a number from both sides of the equation. This helps in eliminating any constants that are on the same side as the variable. In our example:
$4m + 9 = -23$
The next step is to subtract 9 from both sides. This is written mathematically as:
$4m + 9 - 9 = -23 - 9$
Simplifying this, we get:
$4m = -32$
Now, the equation is much closer to isolating the variable because the number 9 has been removed from the left side. Subtraction helps in systematically breaking down the equation by eliminating numbers that are not attached to the variable.

Dividing by a Coefficient

With the equation simplified to $4m = -32$, the final step is to solve for the variable $m$. Since $m$ is being multiplied by 4, we need to do the opposite operation to isolate $m$, which is division. We divide both sides by 4:
$ \frac{4m}{4} = \frac{-32}{4} $
This simplifies to:
$m = -8$
Dividing by the coefficient (the number attached to the variable) is an essential step in solving linear equations. It ensures that the variable stands alone and we can clearly see its value. Always remember, whatever operation you do to one side of the equation, you must do to the other. This maintains the balance and equality of the equation.

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91影视

Solve the equation for the variable. $$4 m+9=-23$$

Short Answer

Step by step solution

Isolate the Variable Term

Solve for the Variable

Key Concepts

Isolating the Variable

Subtracting from Both Sides

Dividing by a Coefficient

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