Question

solve for b and graph the solution.
-105 = -7|b - 840|
click to select points on the number line.

Explanation:

Step1: Divide both sides by -7

To isolate the absolute - value expression, we divide both sides of the equation \(-105=-7|b - 840|\) by \(-7\).
\(\frac{-105}{-7}=\frac{-7|b - 840|}{-7}\)
Simplifying both sides, we get \(15 = |b - 840|\)

Step2: Solve the absolute - value equation

The absolute - value equation \(|x|=a\) (where \(a\geq0\)) has two solutions: \(x = a\) or \(x=-a\).
For \(|b - 840| = 15\), we have two cases:
Case 1: \(b-840=15\)
Add 840 to both sides of the equation: \(b=15 + 840=855\)
Case 2: \(b - 840=-15\)
Add 840 to both sides of the equation: \(b=-15 + 840 = 825\)

Answer:

The solutions for \(b\) are \(b = 825\) and \(b=855\)

To graph the solution on the number line, we mark the points 825 and 855.