Question

Finding Solutions

The solution is k =
Use the work shown below to solve.
1. Identify the operation in the equation
2. Use inverse operations to solve,
Subtraction property of equality
=k+11
13
2
2
15
2
Addition property of equality
+(-)=k+1+(-)

Answer 1

`k = -4`

Explanation:

Given

`(3)/(2) = k + (11)/(2)`

Required

Solve for k

`(3)/(2) = k + (11)/(2)`

Apply subtraction property

`(3)/(2) - (11)/(2) = k + (11)/(2) - (11)/(2)`

Apply addition property

`(3)/(2) +(- (11)/(2)) = k + (11)/(2) +(- (11)/(2) )`

The fractions on the right represent an additive inverse.

So, we have:

`(3)/(2) +(- (11)/(2)) = k`

Take LCM

`(3+(-11))/(2) = k`

Remove bracket

`(3-11)/(2) = k`

`(-8)/(2) = k`

`-(8)/(2) = k`

`-4 = k`

`k = -4`