How do you solve and graph #abs(m-2)

Question

How do you solve and graph #abs(m-2)<8#?

Julia Adams · Accepted Answer

#f(m)={(m-10color(white)("xxx") {m:m>=2}),(-m-6color(white)("xxx") {m:m<2}):}#

for #dom f in (-oo,0)# Recall that for a modulus function #f(x)=|x|#, #f(x)=x# for #x>=0# and #f(x)=-x# for #x<0#. #|m-2| < 8# #:. |m-2| - 8 < 0|# If we call this a function #f(m) = |m-2|-8# for #dom f in (-oo,0)# then we can define it as a hybrid function, which follows the standard transformations of a function, we get: #f(m)={((m-2)-8color(white)("xxx") {m:m>=2}),(-(m-2)-8color(white)("xxx") {m:m<2}):}# #:. f(m)={(m-10color(white)("xxx") {m:m>=2}),(-m-6color(white)("xxx") {m:m<2}):}# Of course, given the domain, we need only consider the function #g(m)=-m-6#, so to sketch, simply draw a straight line from the point #(0,-6)# remembering to leave an open circle at that coordinate.

Abigail Allen · Answer

undefined To solve and graph the inequality abs(m - 2) < 8, you first isolate the absolute value expression, then split it into two cases, and finally graph the solutions on a number line.

Case 1: $ m - 2 \geq 0 $
$ m - 2 < 8 $
$ m < 10 $

Case 2: $ m - 2 < 0 $
$ -(m - 2) < 8 $
$ -m + 2 < 8 $
$ -m < 6 $
$ m > -6 $

Combining both cases:
$ -6 < m < 10 $

On the number line, draw an open circle at -6 and 10, and shade the region between them to represent the solutions.

Eva Abramson · Answer

undefined To solve and graph the inequality $|m - 2| < 8$, follow these steps: 1. Set up two inequalities: a. $m - 2 < 8$ b. $m - 2 > -8$ 2. Solve each inequality separately: a. For $m - 2 < 8$, add 2 to both sides: $m < 10$ b. For $m - 2 > -8$, add 2 to both sides: $m > -6$ 3. Combine the solutions: The solution set for $|m - 2| < 8$ is $-6 < m < 10$. 4. Graph the solution on a number line: Mark -6 and 10 on the number line and draw an open circle at each point because the inequality is strict. Then shade the region between -6 and 10. This represents all the values of $m$ that satisfy the inequality $|m - 2| < 8$.

How do you solve and graph #abs(m-2)&lt;8#?

How do you solve and graph #abs(m-2)<8#?