Problem 95 Solve each equation. $$ 6 x+... [FREE SOLUTION]

Chapter 10: Problem 95

Solve each equation. $$ 6 x+13=0 $$

Short Answer

Expert verified

x = \frac{-13}{6}

Step by step solution

- Isolate the variable term

To solve for the variable x, start by isolating the term containing x. Subtract 13 from both sides of the equation: \[ 6x + 13 - 13 = 0 - 13 \] This simplifies to \[ 6x = -13 \]

- Solve for x

Now, solve for x by dividing both sides of the equation by 6: \[ x = \frac{-13}{6} \]

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Key Concepts

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

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. Linear equations are equations of the first degree, meaning they have no exponents other than one. For example, in the equation 6x + 13 = 0, 'x' is our variable.

To solve a linear equation, you generally follow these steps:

Identify the variable that you need to solve for.
Isolate the variable term by performing basic arithmetic operations like addition, subtraction, multiplication, or division on both sides of the equation.
Simplify the equation until you have the variable alone on one side of the equation.
Check your solution by substituting it back into the original equation.

Isolation of Variables

Isolation of variables means getting the variable alone on one side of the equation. This is usually the first step in solving linear equations.

Let's break down how to isolate the variable in the given problem:
1. Start with the equation 6x + 13 = 0.
2. To isolate x, you first need to eliminate the constant term (which is 13) by subtracting it from both sides. This looks like 6x + 13 - 13 = 0 - 13.
3. Once you perform the subtraction, you get 6x = -13.

Now, you have a simpler equation where the term containing the variable (6x) is isolated. Next, you solve for the variable by performing further operations.

Basic Algebra

Basic algebra includes fundamental concepts and operations like addition, subtraction, multiplication, and division. These are essential when solving linear equations.

In the second step for our example:

We have 6x = -13.
To solve for x, you need to remove the coefficient (which is 6) that's multiplied by the variable.
To do this, you divide both sides of the equation by 6.
So, x = -13/6.

Basic algebra principles ensure that whatever operation you do to one side of the equation, you must do to the other side as well. This keeps the equation balanced and maintains equality between both sides.

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91影视

Solve each equation. $$ 6 x+13=0 $$

Short Answer

Step by step solution

- Isolate the variable term

- Solve for x

Key Concepts

Solving Linear Equations

Isolation of Variables

Basic Algebra

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