Question

solve for d and graph the solution.\
\\(-8|d - 90| = -80\\)\
click to select points on the number line.\
number line from 0 to 100 with ticks at 0,10,20,30,40,50,60,70,80,90,100\
submit

Explanation:

Step1: Divide both sides by -8

To isolate the absolute value expression, we divide both sides of the equation \(-8|d - 90| = -80\) by \(-8\).

$$ \frac{-8|d - 90|}{-8}=\frac{-80}{-8} $$

Simplifying both sides gives:

$$ |d - 90| = 10 $$

Step2: Solve the absolute value equation

The absolute value equation \(|d - 90| = 10\) means that \(d - 90 = 10\) or \(d - 90 = -10\) (because the absolute value of a number is its distance from zero, so it can be positive or negative the given value).

For \(d - 90 = 10\):

Add 90 to both sides of the equation:

$$ d - 90 + 90 = 10 + 90 $$

$$ d = 100 $$

For \(d - 90 = -10\):

Add 90 to both sides of the equation:

$$ d - 90 + 90 = -10 + 90 $$

$$ d = 80 $$

Answer:

The solutions for \(d\) are \(d = 80\) and \(d = 100\). To graph the solution, we would mark the points 80 and 100 on the number line (the given number line has marks at 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, so we select 80 and 100).