Problem 1 Is $-11$ a solution of \(2 x+3... [FREE SOLUTION]

91影视

Prealgebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 2: Problem 1

Is $-11$ a solution of $2 x+3=-19 ?$

Short Answer

Expert verified

Yes, -11 is a solution because it satisfies the equation.

Step by step solution

Substitute \$x = -11\$

First, we need to substitute $x = -11$ into the equation $2x + 3 = -19$. This means replacing the $x$ in the equation with $-11$. So, the equation becomes: $(2 imes -11) + 3 = -19$.

Simplify the Expression

Now, simplify the expression \[2 imes -11 + 3\].Calculate $2 imes -11$, which equals $-22$. Then, add $3$ to $-22$, resulting in $-19$.

Check Equality

The simplified expression gives us $-19$. Now compare it to the right side of the equation: $-19$. Both sides of the equation are equal, $-19 = -19$, which means the substitution holds true.

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Key Concepts

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

Substitution Method

When solving linear equations, one of the most important techniques is the substitution method. This involves replacing a variable with a given value in the equation. It helps us check if this value satisfies the equation. In our given problem, we are asked if $-11$ is a solution for the equation $2x + 3 = -19$.
By substituting the value $-11$ for $x$, we rewrite the equation as $2(-11) + 3 = -19$. This step allows us to see the result of the expression when $x = -11$.

Identify the variable to replace, which in this case is $x$.
Substitute the given value into the equation.

Using substitution is like testing a theory: if the substitution results in a true statement, it confirms that the provided value is indeed a solution.

Simplification

Simplification is all about making a mathematical expression more manageable by combining like terms and performing basic operations. In the context of our problem, after substituting the value of $x$, we now have the expression $2 \times -11 + 3$.
First, calculate $2 \times -11$. This results in $-22$.
Next, add $3$ to $-22$. The result is $-19$. This process of simplification helps in reducing the equation to a clearer form.

Perform multiplication before addition or subtraction, following the order of operations.
Combine terms to ensure you have simplified as much as possible.

By simplifying, you ensure that the complexity of the problem does not cloud your judgment about the accuracy of your solution.

Checking Solutions

Checking solutions is a crucial final step in verifying whether a particular value satisfies an equation. After simplification, we found that the expression $2 \times -11 + 3$ simplifies to $-19$.
This step involves comparing this result with the right side of the original equation. Since both sides are equal $-19 = -19$, this confirms that $x = -11$ is indeed a solution to the equation $2x + 3 = -19$.

Always compare the result of the simplification with the constant term on the other side of the equation.
If both sides are equal, the substitution has been successful.

Checking your solutions reinforces the accuracy and ensures that the steps you've followed are correct. It verifies the solution before you conclude the problem.

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91影视

Is \(-11\) a solution of \(2 x+3=-19 ?\)

Short Answer

Step by step solution

Substitute \\(x = -11\\)

Simplify the Expression

Check Equality

Key Concepts

Substitution Method

Simplification

Checking Solutions

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