College

Solve for [tex] f [/tex] in the following equation:

\[ 85 = 7.4 + f + 10.2 \]

Solve for [tex] n [/tex] in the following equation:

\[ n - \$32 = \$82 \]

Answer :

Sure! Let's solve the equation step by step to find the value of [tex]\( n \)[/tex].

We are given the equation:

[tex]\[ n - 32 = 82 \][/tex]

To solve for [tex]\( n \)[/tex], we need to get [tex]\( n \)[/tex] by itself on one side of the equation. Here’s how we can do that:

1. Identify the operation involving [tex]\( n \)[/tex]: In this equation, 32 is subtracted from [tex]\( n \)[/tex].

2. Undo the subtraction by performing the opposite operation: Add 32 to both sides of the equation to cancel out the [tex]\(-32\)[/tex] on the left side.

So, add 32 to both sides:

[tex]\[
n - 32 + 32 = 82 + 32
\][/tex]

3. Simplify both sides:

The left side simplifies to [tex]\( n \)[/tex] because [tex]\(-32 + 32\)[/tex] is 0:

[tex]\[
n = 82 + 32
\][/tex]

4. Calculate the sum on the right side:

[tex]\[
n = 114
\][/tex]

So, the solution to the equation [tex]\( n - 32 = 82 \)[/tex] is [tex]\( n = 114 \)[/tex].