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

Start with (1/2)x + 4 = −(1/2)x + 4. Subtract 4: (1/2)x = −(1/2)x. Add (1/2)x to both sides: x = 0.

Answer: 0.