Question

solve for s.
5s - 9 = 3s + 5
simplify.
\frac{\sqrt{45}}{7}

Explanation:

First Problem: Solve for \( s \) in \( 5s - 9 = 3s + 5 \)

Step 1: Subtract \( 3s \) from both sides

To get the \( s \)-terms on one side, we subtract \( 3s \) from both sides of the equation. This gives us \( 5s - 3s - 9 = 3s - 3s + 5 \), which simplifies to \( 2s - 9 = 5 \).

Step 2: Add 9 to both sides

Next, we add 9 to both sides to isolate the term with \( s \). So, \( 2s - 9 + 9 = 5 + 9 \), which simplifies to \( 2s = 14 \).

Step 3: Divide by 2

Finally, we divide both sides by 2 to solve for \( s \). \( \frac{2s}{2} = \frac{14}{2} \), so \( s = 7 \).

Step 1: Factor 45

First, we factor 45 into its prime factors. \( 45 = 9 \times 5 \), and 9 is a perfect square (\( 9 = 3^2 \)).

Step 2: Simplify the square root

Using the property of square roots \( \sqrt{ab} = \sqrt{a} \times \sqrt{b} \) (where \( a \) is a perfect square), we can simplify \( \sqrt{45} \) as \( \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} \).

Step 3: Substitute back

Now we substitute this simplified square root back into the original fraction. So \( \frac{\sqrt{45}}{7} = \frac{3\sqrt{5}}{7} \).

Answer:

\( s = 7 \)

Second Problem: Simplify \( \frac{\sqrt{45}}{7} \)