Problem 66 Is $-18$ a solution to the equ... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 8: Problem 66

Is $-18$ a solution to the equation $3 x=16-5 x ?$ How do you know?

Short Answer

Expert verified

-18 is not a solution because -54 does not equal 106.

Step by step solution

- Understand the Equation

The given equation is: 3x = 16 - 5x. The goal is to determine if -18 is a solution to this equation.

- Substitute the Value of x

Replace the variable x with -18 in the equation: 3(-18) = 16 - 5(-18).

- Simplify Both Sides

First, simplify the left-hand side of the equation: 3(-18) = -54 . Next, simplify the right-hand side of the equation: 16 - 5(-18) = 16 + 90 = 106.

- Compare the Results

After simplification, the equation becomes: -54 = 106 . The two sides of the equation are not equal, therefore -18 is not a solution to the equation.

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Key Concepts

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

Equation Simplification

Simplification is the process of making an equation easier to work with by performing basic mathematical operations.
Simplifying an equation helps to clearly see the relationships between variables and constants.
In our case, we start with the equation: 3x = 16 - 5x.
To simplify, we move all terms involving x to one side of the equation.
We add 5x to both sides to get: 3x + 5x = 16.
This combines the x terms: 8x = 16.
Next, we divide both sides by 8 to isolate x: x = 2.
This process makes the equation simpler to solve.

Substitution Method

The substitution method is used to verify potential solutions by replacing the variable with a given value.
To know if -18 is a solution to the equation 3x = 16 - 5x, we substitute -18 for x.
After substitution, the equation becomes: 3(-18) = 16 - 5(-18).
Simplify both sides: 3(-18) = -54,16 - 5(-18) = 16 + 90 = 106.
Comparing both sides, we get -54 鈮� 106.
This shows that substituting -18 into the equation does not satisfy it, hence, -18 is not a solution.

Solution Verification

Solution verification is the step where we confirm if a substituted value satisfies the original equation.
It helps to ensure we have the correct solution.
To verify, we substitute the value back into the equation and check if both sides are equal.
In our example: 3(-18) = 16 - 5(-18).
After simplifying, we get: -54 = 106.
Since the results do not match, we conclude that -18 is not a solution.
Verification clearly demonstrates whether the solution is correct or not. It is a crucial step in ensuring accuracy.

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91影视

Is \(-18\) a solution to the equation \(3 x=16-5 x ?\) How do you know?

Short Answer

Step by step solution

- Understand the Equation

- Substitute the Value of x

- Simplify Both Sides

- Compare the Results

Key Concepts

Equation Simplification

Substitution Method

Solution Verification

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