Problem 112 - Elementary Algebra

Question

Solve: \(9 x=0\)

Step-by-Step Solution

Answer

x = 0

Step 1: Identify the Equation

Start by writing down the given equation: \[9x = 0\]

Step 2: Isolate the Variable

To solve for \(x\), divide both sides of the equation by 9: \[\frac{9x}{9} = \frac{0}{9}\] This simplifies to: \[x = 0\]

Key Concepts

isolate the variable

When you're solving a linear equation, the first essential step is to **isolate the variable**. This means getting the variable by itself on one side of the equation.
In our example, we have the equation \( 9x = 0 \). We need to get 'x' by itself to find its value.
To do this, we identify the part of the equation that combines with the variable, which here is the number 9 (or multiplying by 9). By removing this component, we isolate 'x'.
This step is crucial for solving all algebraic equations. Properly isolating the variable paves the way for further simplification.

divide both sides

After identifying the part of the equation containing the variable, the next step is often to **divide both sides** of the equation by a specific number.
This is done to eliminate the coefficient attached to the variable. For example, we have \( 9x = 0 \). Here, '9' is multiplied by 'x'.
To isolate 'x', we divide both sides by '9':

• \( \frac{9x}{9} = \frac{0}{9} \)

Dividing both sides helps to keep the equation balanced and simplifies our work.

simplify equations

The final step in solving linear equations involves **simplifying the equations**.
Once both sides are divided, simplification brings us closer to the solution. From the previous step, we have: \frac{9x}{9} = \frac{0}{9}.
We simplify this by canceling out the common factors (9 in this case), leaving us with the simple result:

• \( x = 0 \)

By simplifying, we obtain the final value of the variable. This step ensures clarity and accuracy in finding the solution.