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Chapter 2: Problem 21

Solve equation, and check your solution. \(6 x=36\)

Short Answer

Expert verified
x = 6

Step by step solution

01

Isolate the Variable

To solve for the variable, we need to isolate it on one side of the equation. Since the variable is multiplied by 6, divide both sides of the equation by 6: \(\frac{6x}{6} = \frac{36}{6}\)
02

Simplify the Equation

Simplify both sides of the equation: \( x = 6 \)
03

Check the Solution

Substitute the solution back into the original equation to verify it: \( 6(6) = 36 \) Since both sides of the equation are equal, our solution is correct.

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Key Concepts

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

Isolate the Variable
To solve a linear equation, the first step is isolating the variable. This means getting the variable you need to solve for, such as 'x', by itself on one side of the equation.
In the given problem, we have the equation: \(6x = 36\).
The variable 'x' is currently multiplied by 6. To isolate 'x', we need to eliminate the factor of 6 on the left side. We do this by performing the inverse operation - division. Because of the multiplication by 6, we divide both sides of the equation by 6: \[ \frac{6x}{6} = \frac{36}{6} \]
Dividing both sides balances the equation and isolates the variable. Now we have: \[ x = 6 \]
Simplify the Equation
Once we've isolated the variable, the next step is to simplify the equation. Simplifying ensures that the variable 'x' is alone and the equation is in its simplest form. From our earlier step, we have: \[ x = 6 \]
Here, the equation is already simplified because 'x' is expressed without additional terms or factors. Simplification is about making the math as straightforward as possible. Always remember:
  • Combine like terms
  • Perform basic arithmetic operations, such as addition, subtraction, multiplication, and division
  • Ensure the variable stands alone, if possible
At this stage, our solution is straightforward and simplified, with 'x' isolated as 6.
Check the Solution
The final step is to check the solution. Verifying your answer ensures that the solution correctly satisfies the original equation. To check the solution 'x=6', we substitute it back into the original equation: \[ 6(6) = 36 \]
If this substitution holds true, then our solution is correct. Performing the multiplication: \[ 36 = 36 \]
Since both sides of the equation are equal, it confirms that our solution, x = 6, is indeed correct. Double-checking your work gives you confidence in the accuracy of your solution and helps catch any possible mistakes.
So, the key steps in checking your solution include:
  • Substitute the found value back into the original equation
  • Perform the necessary calculations
  • Verify that both sides of the equation are equal
This process affirms that you have correctly solved the equation.

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