Problem 55 - Prealgebra

Question

Solve each equation. Check your solution. $$32.76=5.2 s$$

Step-by-Step Solution

Answer

The solution is \( s = 6.3 \). Substitution confirms the correctness.

Step 1: Isolate the Variable

We need to solve for the variable \( s \). To do this, we'll divide both sides of the equation by \( 5.2 \) to isolate \( s \). This gives us: \[ s = \frac{32.76}{5.2} \]

Step 2: Perform the Division

Now, perform the division \( \frac{32.76}{5.2} \). To make it easier, you can calculate it using a calculator or by long division:- Perform the division and you get \( s = 6.3 \).

Step 3: Check the Solution

To verify the solution, substitute \( s = 6.3 \) back into the original equation:- Calculate \( 5.2 \times 6.3 = 32.76 \).- The result is equal to the left side of the original equation \( 32.76 \), confirming that \( s = 6.3 \) is correct.

Key Concepts

Isolate the Variable

Understanding how to isolate the variable in an equation is key to solving it. When dealing with equations, our goal is to solve for the variable. In this case, the variable is \( s \). To isolate \( s \), we must manipulate the equation so that \( s \) stands alone on one side of the equation.

• Start with the equation: \( 32.76 = 5.2s \).
• To get \( s \) by itself, we need to "undo" whatever is being done to \( s \). Here, \( s \) is being multiplied by \( 5.2 \).
• Perform the opposite operation of multiplication, which is division, to both sides of the equation.

This results in \( s = \frac{32.76}{5.2} \). By isolating the variable, we've set up the equation for the next step, division.

Division

After you've successfully isolated the variable, the next step is performing the division. This step is crucial as it directly yields the value of the variable.

• You now have the equation \( s = \frac{32.76}{5.2} \).
• Division will determine the value of \( s \). You can use long division or a calculator to find the answer.
• When you calculate \( \frac{32.76}{5.2} \), you find that \( s = 6.3 \).

Performing division accurately is essential to ensure the correctness of your solution. Consider checking your arithmetic or using a calculator, as precision is key.

Verify Solution

Verifying your solution is the final step in equation solving and it ensures the accuracy of your answer.

• Start by substituting the value you found for \( s \) back into the original equation.
• The original equation is \( 32.76 = 5.2s \). Substituting \( s = 6.3 \), we perform the multiplication: \( 5.2 \times 6.3 = 32.76 \).
• If both sides of the equation are equal, as they are in this case, your solution is verified.

Verifying helps solidify your understanding and boosts confidence that the solution is correct. It's an important habit to develop when solving equations.