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Chapter 1: Problem 19

Solve. $$ 8 t=72 $$

Short Answer

Expert verified
The solution is \( t = 9 \).

Step by step solution

01

Identify the equation

The given equation is: \[ 8t = 72 \]
02

Isolate the variable

To solve for \( t \), we need to isolate it on one side of the equation. To do this, we will divide both sides of the equation by 8: \[ \frac{8t}{8} = \frac{72}{8} \]
03

Simplify both sides

Simplify both sides of the equation: \[ t = \frac{72}{8} \] Calculate the division on the right side: \[ t = 9 \]
04

Verify the solution

To ensure that the solution is correct, substitute \( t = 9 \) back into the original equation: \[ 8 \times 9 = 72 \] Since both sides of the equation are equal, \( t = 9 \) is indeed 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, one crucial step is to isolate the variable. This means we want our variable, in this case, 't', to be alone on one side of the equation. Think of it as getting all your toys in one basket.
In the given exercise, the equation is: \(8t = 72\).
To isolate 't', we must get rid of the 8 that is multiplying it. We do this by performing the opposite operation. Since 8 is multiplied by 't,' we divide both sides of the equation by 8. This step looks like this: \( \frac{8t}{8} = \frac{72}{8} \).
After we divide both sides, we are left with 't' all by itself: \(t = \frac{72}{8} \).
Simplify Equations
Once we have isolated the variable, the next step is to simplify the equation. Simplifying means making the equation as simple and clean as possible. In our example, \(t = \frac{72}{8}\), we need to perform the division on the right side.
When we divide 72 by 8, we get: \(t = 9 \).
Simplifying is essential because it reduces a complex problem to a simpler, more understandable form. This makes it easier for us to find the solution.
Verify Solutions
The final step in solving a linear equation is to verify the solution. We do this to ensure our answer is correct. Verification involves substituting the value we found back into the original equation.
In this problem, our solution for 't' was 9. To verify, we substitute 9 back into the original equation: \(8t = 72\). It becomes \(8 \times 9 = 72\).
Simplifying the left side, we get: \(72 = 72\).
Since both sides are equal, our solution of \(t = 9\) is indeed correct. Always verify your solutions to avoid mistakes and confirm your answer.

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