To solve the equation
[tex]\[ -\frac{7}{4} + \frac{x}{4} = 2, \][/tex]
we need to isolate the variable [tex]\( x \)[/tex].
1. Identify the constant term on the left side:
The term [tex]\( -\frac{7}{4} \)[/tex] is the constant term that we need to eliminate from the left side to isolate the variable term.
2. Add the same term to both sides:
To eliminate [tex]\( -\frac{7}{4} \)[/tex], we add [tex]\( \frac{7}{4} \)[/tex] to both sides of the equation:
[tex]\[
-\frac{7}{4} + \frac{x}{4} + \frac{7}{4} = 2 + \frac{7}{4}.
\][/tex]
3. Simplify the equation:
On the left side, [tex]\( -\frac{7}{4} + \frac{7}{4} \)[/tex] cancels out, leaving:
[tex]\[
\frac{x}{4} = 2 + \frac{7}{4}.
\][/tex]
Therefore, the property of operations that allows us to add the same constant term to both sides of an equation is the addition property of equality.
