Problem 169 Solve the linear equation using ... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 8: Problem 169

Solve the linear equation using the general strategy. $$-7(3 n+4)=14$$

Short Answer

Expert verified

n = -2.

Step by step solution

- Distribute the constant

Apply the distributive property to the left-hand side of the equation: $-7(3n + 4) = 14$. This gives: $-21n - 28 = 14$.

- Add 28 to both sides

To isolate the term with the variable, add 28 to both sides of the equation: $-21n - 28 + 28 = 14 + 28$. This simplifies to: $-21n = 42$.

- Divide by -21

Solve for $n$ by dividing both sides of the equation by $-21$: $n = \frac{42}{-21}$. This gives: $n = -2$.

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Key Concepts

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

Distributive Property

The distributive property is a key idea in algebra that helps simplify expressions and equations.
It states that multiplying a sum or difference by a number is the same as multiplying each term within the parentheses by that number and then adding or subtracting the results.
In the given exercise, we see this property in action with the equation $-7(3n + 4) = 14$.
To apply the distributive property, we multiply \-7 by each term inside the parentheses:
$-7 \times 3n + (-7) \times 4 = -21n - 28$.
This step simplifies the problem, making it easier to solve for the variable.

Isolate Variables

Isolating the variable is an essential part of solving linear equations.
The goal is to get the variable by itself on one side of the equation.
In the example equation \-21n - 28 = 14\, we want to isolate \.
To do this, we perform operations to eliminate other terms and coefficients from the side where \ is located.
We start by adding 28 to both sides of the equation to cancel out the \-28\:
$-21n - 28 + 28 = 14 + 28$.
This simplifies to \-21n = 42\.
Now, \ is closer to being isolated.

Solving Equations Step by Step

Solving equations step by step allows us to break down complex problems into manageable parts.
Follow these steps to solve a linear equation:

Apply the distributive property to remove parentheses.
Combine like terms, if necessary.
Isolate the variable using addition or subtraction.
Solve for the variable by dividing both sides of the equation by its coefficient.

In the final step of our example, we divide both sides by \-21\ to isolate \:
$-21n / -21 = 42 / -21$.
This simplifies to \ = -2\, giving us the solution to the equation.

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91影视

Solve the linear equation using the general strategy. $$-7(3 n+4)=14$$

Short Answer

Step by step solution

- Distribute the constant

- Add 28 to both sides

- Divide by -21

Key Concepts

Distributive Property

Isolate Variables

Solving Equations Step by Step

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