Question

For the function 2h(x) - x - 7 = 0, two ordered pairs are (a, 7.5) and (b, 6.5). Find a - b.

Answer 1

The given function is $2h\left(x\right)-x-7=0.$
$\Rightarrow h\left(x\right)=\frac{x+7}{2}=y$

Ordered pair is represented as $(x,y)$
Given ordered pairs are $(a,7.5)$ and $(b,6.5).$
$\therefore x=a$ and $x=b$ corresponds to $y=7.5$ and $y=6.5,$ respectively,
Substitute $y$ in the given function and solve for $x.$

For $y=7.5,$

$\frac{x+7}{2}=7.5$
$\Rightarrow x+7=7.5\times 2=\frac{15}{2}\times 2=15$
$\Rightarrow x=15-7=8$
$\Rightarrow a=8$

For $y=7.5,$

$\frac{x+7}{2}=6.5$
$\Rightarrow x+7=6.5\times 2=\frac{13}{2}\times 2=13$
$\Rightarrow x=13-7=6$
$\Rightarrow b=6$

$\therefore a-b=8-6=2$