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How many solutions does this equation have?

[tex]\[ -17f + 13 = 8 + 5 - 17f \][/tex]

A. No solution
B. One solution
C. Infinitely many solutions

Answer :

To determine how many solutions the equation [tex]\(-17f + 13 = 8 + 5 - 17f\)[/tex] has, let's simplify both sides of the equation and see what we get.

1. Simplify the Right Side of the Equation:
[tex]\[
8 + 5 - 17f = 13 - 17f
\][/tex]

2. Write down the Equation Again with Simplified Right Side:
[tex]\[
-17f + 13 = 13 - 17f
\][/tex]

3. Compare Both Sides:
Notice that both sides of the equation are the same: [tex]\(-17f + 13 = 13 - 17f\)[/tex].

4. Analyze the Equation:
Since both sides are identical, it means that whatever value [tex]\(f\)[/tex] takes, both sides will always equal each other. This indicates that there isn't a single solution but rather infinitely many solutions.

So, the equation [tex]\(-17f + 13 = 8 + 5 - 17f\)[/tex] has infinitely many solutions. This is because the left side is always equal to the right side for any value of [tex]\(f\)[/tex].

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