Problem 65 Solve and check. $$-3 x=6$$... [FREE SOLUTION]

Chapter 5: Problem 65

Solve and check. $$-3 x=6$$

Short Answer

Expert verified

The solution to the equation $-3x = 6$ is $x = -2$.

Step by step solution

Apply Inverse Operation

Since $-3$ is multiplied by $x$, apply multiplication's inverse, which is division, to both sides of the equation. So divide both sides of the equation by $-3$. The equation becomes $x = \frac{6}{-3}$

Simplify the Solution

Simplify the right side of the equation to find the value of $x$. Hence, $x = -2$

Check the Solution

Substitute $x = -2$ back into the original equation $-3 x = 6$. By substituting, the equation becomes $-3*-2 = 6$. By simplifying, the left side of the equation becomes 6. Thus we have verified that our solution is correct because both sides of the equation are equal.

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Key Concepts

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

Inverse Operations and Their Role in Solving

In mathematics, understanding inverse operations is key to solving equations. When dealing with a linear equation, an inverse operation helps us isolate the variable and find its value.
An inverse operation essentially reverses the effect of an operation. For example, multiplication and division are inverse operations because they undo each other.

In the given equation $-3x = 6$, multiplication is involved.
To solve for $x$, we must undo the multiplication by applying its inverse鈥攄ivision.
Thus, we divide both sides by $-3$ and solve for $x$.

This step ensures the equation remains balanced, bringing us closer to the solution. The usage of inverse operations allows us to methodically eliminate operations affecting the variable, leading us directly to its value.

Solving Equations Step by Step

Solving equations involves breaking down the problem using systematic steps, which reveal the value of the variable. When approaching an equation such as $-3x = 6$, the first step is to identify the operation acting on the variable.

In this particular instance, $x$ is multiplied by $-3$.
To isolate $x$, we divide both sides by $-3$, obtaining the equation $x = \frac{6}{-3}$.
The next step is to simplify the right side to find $x$. Hence, $x = -2$.

By following these clear and logical steps, complex equations are made simple. Solving a linear equation becomes a straightforward task when we eliminate operations step by step until the variable stands alone, revealing its value.

Solution Verification: Ensuring Correctness

After solving an equation, it's vital to verify the solution to ensure it's correct. Verification gives us confidence in our solution and confirms our understanding of the process. This process involves substituting the solution back into the original equation and checking for equality.

For the equation $-3x = 6$ and the solution $x = -2$, substitute back into the equation.
The equation becomes $-3*(-2) = 6$.
Simplifying the left side gives us 6, which matches the right side.

This confirmation shows that the solution is accurate, as both sides of the equation are equal. Verification is a crucial step in solving equations, as it checks our solution and reinforces our ability to apply inverse operations correctly.

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91影视

Solve and check. $$-3 x=6$$

Short Answer

Step by step solution

Apply Inverse Operation

Simplify the Solution

Check the Solution

Key Concepts

Inverse Operations and Their Role in Solving

Solving Equations Step by Step

Solution Verification: Ensuring Correctness

One App. One Place for Learning.

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