Question

write an equivalent equation for 2n + 8 = 20
2n + 1 = 8n + 1
d) 5n = 15
image of a balance scale with blocks labeled 5 on the left
e an equivalent equation for 5n = 15

Explanation:

To find an equivalent equation for \( 5n = 15 \), we can perform operations that maintain the equality. One common operation is dividing both sides by a non - zero number or multiplying both sides by a non - zero number, or adding/subtracting the same value from both sides. Here, we'll use division.

Step 1: Divide both sides by 5

If we divide both sides of the equation \( 5n=15 \) by 5, we use the property of equality which states that if \( a = b \), then \( \frac{a}{c}=\frac{b}{c} \) for \( c
eq0 \).
\( \frac{5n}{5}=\frac{15}{5} \)

Step 2: Simplify both sides

Simplifying the left - hand side \( \frac{5n}{5} \) gives us \( n \), and simplifying the right - hand side \( \frac{15}{5} \) gives us 3. So we get the equivalent equation \( n = 3 \).

We can also multiply both sides by a non - zero number. For example, multiply both sides by 2:

Step 1: Multiply both sides by 2

Using the property of equality \( a = b\Rightarrow a\times c=b\times c \) (where \( c = 2\) and \( c
eq0 \)), we have \( 5n\times2=15\times2 \)

Step 2: Simplify both sides

Simplifying the left - hand side \( 5n\times2 = 10n \) and the right - hand side \( 15\times2=30 \). So we get the equivalent equation \( 10n = 30 \)

If we want a simple equivalent equation, one of them is \( n = 3 \) (by dividing both sides by 5) or \( 10n=30 \) (by multiplying both sides by 2). If we take the first method (dividing by 5):

Answer:

\( n = 3 \) (or other equivalent equations like \( 10n = 30 \) can also be correct depending on the operation used)