High School

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How many solutions does this equation have?

[tex]-19 + 15c = 17c + 20 - 11[/tex]

A. One solution
B. Infinitely many solutions

Answer :

We start with the given equation:

[tex]$$
-19 + 15c = 17c + 20 - 11.
$$[/tex]

Step 1. Simplify the right side.
Calculate the constant on the right side:

[tex]$$
20 - 11 = 9.
$$[/tex]

So the equation becomes:

[tex]$$
-19 + 15c = 17c + 9.
$$[/tex]

Step 2. Isolate the variable terms.
Subtract [tex]$15c$[/tex] from both sides to get the variable terms on one side:

[tex]$$
-19 = 17c - 15c + 9.
$$[/tex]

This simplifies to:

[tex]$$
-19 = 2c + 9.
$$[/tex]

Step 3. Isolate the constant with the variable.
Subtract [tex]$9$[/tex] from both sides:

[tex]$$
-19 - 9 = 2c,
$$[/tex]

which gives:

[tex]$$
-28 = 2c.
$$[/tex]

Step 4. Solve for [tex]$c$[/tex].
Divide both sides by [tex]$2$[/tex]:

[tex]$$
c = \frac{-28}{2} = -14.
$$[/tex]

Since we arrived at a unique value [tex]$c = -14$[/tex], the equation has exactly one solution.

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