Answer:
[tex]k = -4[/tex]
Step-by-step explanation:
Given
[tex]\frac{3}{2} = k + \frac{11}{2}[/tex]
Required
Solve for k
[tex]\frac{3}{2} = k + \frac{11}{2}[/tex]
Apply subtraction property
[tex]\frac{3}{2} - \frac{11}{2} = k + \frac{11}{2} - \frac{11}{2}[/tex]
Apply addition property
[tex]\frac{3}{2} +(- \frac{11}{2}) = k + \frac{11}{2} +(- \frac{11}{2} )[/tex]
The fractions on the right represent an additive inverse.
So, we have:
[tex]\frac{3}{2} +(- \frac{11}{2}) = k[/tex]
Take LCM
[tex]\frac{3+(-11)}{2} = k[/tex]
Remove bracket
[tex]\frac{3-11}{2} = k[/tex]
[tex]\frac{-8}{2} = k[/tex]
[tex]-\frac{8}{2} = k[/tex]
[tex]-4 = k[/tex]
[tex]k = -4[/tex]
