What is the solution to this equation?
30.16=17.56+5x
The Correct answer and Explanation is:
To solve the equation 30.16=17.56+5×30.16 = 17.56 + 5×30.16=17.56+5x, we want to isolate the variable xxx. Here’s how to do it step by step:
Step 1: Isolate the term with xxx
Start by moving 17.5617.5617.56 from the right side of the equation to the left side. This can be achieved by subtracting 17.5617.5617.56 from both sides:30.16−17.56=5×30.16 – 17.56 = 5×30.16−17.56=5x
Step 2: Perform the subtraction
Now, calculate 30.16−17.5630.16 – 17.5630.16−17.56:30.16−17.56=12.6030.16 – 17.56 = 12.6030.16−17.56=12.60
Now the equation looks like this:12.60=5×12.60 = 5×12.60=5x
Step 3: Solve for xxx
Next, to isolate xxx, divide both sides of the equation by 555:x=12.605x = \frac{12.60}{5}x=512.60
Step 4: Perform the division
Calculating 12.60÷512.60 \div 512.60÷5:x=2.52x = 2.52x=2.52
Final Solution
Thus, the solution to the equation 30.16=17.56+5×30.16 = 17.56 + 5×30.16=17.56+5x isx=2.52x = 2.52x=2.52
Explanation
In algebra, solving equations often involves isolating the variable on one side. This process typically includes basic arithmetic operations—addition, subtraction, multiplication, and division.
- Isolating the Variable: We began by moving all terms that do not include the variable to the opposite side. In our case, we subtracted 17.5617.5617.56 from both sides to isolate the term involving xxx.
- Performing Operations: It’s essential to execute arithmetic operations accurately. We ensured that the calculations—both the subtraction and the division—were conducted step by step.
- Dividing: Finally, dividing the resulting number by the coefficient of xxx (which was 555) provided us with the value of xxx.
This method of systematically applying operations to isolate the variable is fundamental in algebra and lays the groundwork for more complex equations in the future. The solution x=2.52x = 2.52x=2.52 indicates that when xxx takes this value, both sides of the original equation will be equal.