Problem 102 Solve each equation. $$ 7 x=... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 6: Problem 102

Solve each equation. $$ 7 x=0 $$

Short Answer

Expert verified

The solution is $x = 0$.

Step by step solution

- Identify the given equation

The given equation is $7x = 0$.

- Isolate the variable

To isolate the variable $x$, divide both sides of the equation by 7. This gives us $x = \frac{0}{7}$.

- Simplify the fraction

Simplify the right-hand side: $x = \frac{0}{7}$. Since any number divided by zero is zero, this simplifies to $x = 0$.

- Verify the solution

Substitute $x = 0$ back into the original equation to check: $7 \cdot 0 = 0$. This holds true, confirming the solution.

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Key Concepts

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

isolating variables

When solving linear equations, one of the most important steps is to isolate the variable. In this exercise, we need to solve for the variable $x$ in the equation $7x = 0$. This means we want to get $x$ by itself on one side of the equation. To do this, we need to eliminate the $7$ that is being multiplied by $x$. The most straightforward way to achieve this is by performing the opposite operation, which is division. We divide both sides of the equation by $7$, giving us the equation $x = \frac{0}{7}$. This step is crucial as it simplifies the equation, making it easier to find the value of $x$.

simplifying fractions

After isolating the variable, the next step in our solution involves simplifying fractions. In our equation, we are left with $x = \frac{0}{7}$. Simplifying fractions means reducing them to their simplest form. However, in this case, since the numerator is $0$, the fraction itself is already as simple as it gets. Remember, any number divided by $0$ is $0$. So, $\frac{0}{7} = 0$. Understanding how to simplify fractions helps in making complex equations much easier to solve.

verifying solutions

The final step in solving linear equations is to verify the solutions. It's important to check if our solution is correct by substituting it back into the original equation. In our example, we'll substitute $x = 0$ back into the equation $7x = 0$. We replace $x$ with $0$, so the equation becomes $7 \times 0 = 0$. This simplifies to $0 = 0$, which is true. Thus, verifying the solution reassures us that our calculations were correct and that $x = 0$ is indeed the solution to the equation $7x = 0$. Always make sure to go through this step for accurate results.

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91影视

Solve each equation. $$ 7 x=0 $$

Short Answer

Step by step solution

- Identify the given equation

- Isolate the variable

- Simplify the fraction

- Verify the solution

Key Concepts

isolating variables

simplifying fractions

verifying solutions

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