Question

does the equation \\(\frac{1}{2}(2x - 6)=15 - x\\) have one solution, no solutions, or infinitely many solutions? how many solutions does this equation have? solve on paper and enter your answer on zearn. \\(\frac{1}{2}(2x - 6)=15 - x\\) options: infinitely many solutions, one solution, no solutions

Explanation:

Step1: Expand left-hand side

$\frac{1}{2}(2x - 6) = \frac{1}{2} \cdot 2x - \frac{1}{2} \cdot 6 = x - 3$

Step2: Rewrite simplified equation

$x - 3 = 15 - x$

Step3: Isolate x terms

$x + x = 15 + 3$

Step4: Solve for x

$2x = 18$
$x = \frac{18}{2} = 9$
Since we found a single unique value for x, the equation has one solution.

Answer:

One solution, $x=9$