Question

Karissa begins to solve the equation StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis.. Her work is correct and is shown below. Three lines of math. The first line, StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis. The second line, StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half EndFraction x minus x plus 4. The third line StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half EndFraction x plus 4. StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half Endfraction x minus x plus 4. StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half Endfraction x plus 4. When she subtracts 4 from both sides, Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction x. results. What is the value of ? –1 –negative StartFraction one-half EndFraction 0 StartFraction one-half EndFraction.

Answer 1

Option C (0)

Explanation:

Answer 2

x = 0

Explanation:

Given

Karissa begins to solve the equation ...

`(1)/(2)(x-14)+11=(1)/(2)x-(x-4)`

Her work is correct and is shown below. Three lines of math.

`(1)/(2)(x-14)+11=(1)/(2)x-(x-4)\qquad\text{given}\\\\(1)/(2)x-7+11=(1)/(2)x-x+4\qquad\text{eliminate parentheses}\\\\(1)/(2)x+4=-(1)/(2)x+4\qquad\text{collect terms}`

When she subtracts 4 from both sides, the result is ...

`(1)/(2)x=-(1)/(2)x`

Find

What is the value of x?

Solution

Karissa can determine the value of x by adding 1/2x to both sides:

`x=0`