Question

$\frac{1}{4}h + 5 = \frac{1}{4} + 7$
this equation has one solution because the variable terms do not cancel when solving with inverse operations.
this equation has two solutions because $h$ could be positive or negative.
this equation has infinitely many solutions because both expressions have $\frac{1}{4}$.
this equation has no solution because the variable terms cancel and 5 can never be equal to 7.

Explanation:

Step1: Simplify right-hand side

$7+\frac{1}{4}=\frac{28}{4}+\frac{1}{4}=\frac{29}{4}$

Step2: Isolate variable term

$\frac{1}{4}h=\frac{29}{4}-5$
$\frac{1}{4}h=\frac{29}{4}-\frac{20}{4}=\frac{9}{4}$

Step3: Solve for $h$

$h=\frac{9}{4}\times4=9$

Answer:

This equation has one solution because the variable terms do not cancel when solving with inverse operations.