Karissa begins to solve the equation . 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.

When she subtracts 4 from both sides, results. What is the value of ?

–1

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0

Answer:

$\large\boxed{\dfrac{1}{2}x=-\dfrac{1}{2}x\to x=0}$

Step-by-step explanation:

$(1st\ line)\qquad\dfrac{1}{2}(x-14)+11=\dfrac{1}{2}x-(x-4)\qquad\text{use the distributive property}\\\\\dfrac{1}{2}x-\left(\dfrac{1}{2}\right)(14)+11=\dfrac{1}{2}x-x-(-4)\\\\(2nd\ line)\qquad\dfrac{1}{2}x-7+11=\dfrac{1}{2}x-x+4\qquad\text{combine like terms}\\\\(3rd\ line)\qquad\dfrac{1}{2}x+4=-\dfrac{1}{2}x+4\qquad\text{subtract 4 from both sides}\\\\\dfrac{1}{2}x+4-4=-\dfrac{1}{2}x+4-4\\\\\dfrac{1}{2}x=-\dfrac{1}{2}x\qquad\text{add}\ \dfrac{1}{2}x\ \text{to both sides}$

$\dfrac{1}{2}x+\dfrac{1}{2}x=-\dfrac{1}{2}x+\dfrac{1}{2}x\\\\1x=0\to x=0$

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