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Chapter 2: Problem 39

Solve each equation, and check the solution. $$ 0.2 t=8 $$

Short Answer

Expert verified
The solution is t = 40.

Step by step solution

01

Isolate the variable

To isolate the variable t, divide both sides of the equation by 0.2. The equation becomes:\[ t = \frac{8}{0.2} \]
02

Simplify the fraction

Simplify the fraction by multiplying both numerator and denominator by 10 to get rid of the decimal:\[ t = \frac{8 \times 10}{0.2 \times 10} = \frac{80}{2} \]
03

Perform the division

Now, divide 80 by 2 to find the value of t:\[ t = \frac{80}{2} = 40 \]
04

Check the solution

Substitute t back into the original equation to check the solution:\[ 0.2 \times 40 = 8 \]Since this is true, t = 40 is the correct solution.

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Key Concepts

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

Isolate the Variable
When solving linear equations, our goal is to isolate the variable. Here, our variable is \( t \) and the equation is \( 0.2t = 8 \).
To isolate \( t \), we need to remove the coefficient 0.2. We do this by dividing both sides of the equation by 0.2.
This gives us: \( t = \frac{8}{0.2} \).
By isolating the variable, we make it easier to find its exact value.
Simplifying Fractions
Next, we simplify the fraction \( \frac{8}{0.2} \). Simplifying fractions involves making them easier to understand and solve. Here, we'll get rid of the decimal point by multiplying both the numerator and the denominator by 10.
This step transforms the fraction into \( \frac{8 \times 10}{0.2 \times 10} = \frac{80}{2} \).
Now, it's much easier to work with.
Performing the Division
In the final step, we'll perform the division \( \frac{80}{2} \).
This step gives us the solution for the variable: \( t = \frac{80}{2} = 40 \).
To ensure our solution is correct, we substitute \( t = 40 \) back into the original equation. If the left-hand side equals the right-hand side, our solution is validated.
In this case, substituting \( t \) gives \( 0.2 \times 40 = 8 \), confirming that \( t = 40 \) is indeed correct.

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