How do you graph and solve # 3|x-1|+2=8#?

Question

How do you graph and solve # 3|x-1|+2>=8#?

Eli Assouline · Accepted Answer

#(-oo, -1] " U " [ 3, oo) #

#|x| >= k => " " x>= k " " or " " " x<= -k#

#|x| <= k => " " k <=x <= k#
Given:

#3|x-1| +2 >= 8#
Isolate the inequality, so absolute value can be by itself.

Step 1: Subtract 2 to both side

#3|x-1|+cancel(2 color(red)(- 2)) >= 8 color(red)(- 2)#

#3|x-1| >= 6#
Step 2 : Divide by 3 to both side

#(3|x-1|)/color(blue)(3) >= 6/color(blue)(3)#

#|x-1| >= 2#
Step 3 : Undo the absolute value like the information mention at the beginning

#=>x-1 >= 2 " " " " or " " " " x-1 <= -2#

Step 4 : Solve for #x#

# x >= 3 " " " or " " " x<= -1#

Step 5: Draw the number line and determine the interval from Step 4.

Solution: #(-oo, -1] " U " [ 3, oo) #

Jameson Allen · Answer

undefined To graph and solve $3|x-1|+2 \geq 8$, first isolate the absolute value expression:

$$3|x-1| \geq 6$$

Then, divide both sides by 3:

$$|x-1| \geq 2$$

This means that either $x-1 \geq 2$ or $x-1 \leq -2$:

For $x-1 \geq 2$:
$$x-1 \geq 2$$
$$x \geq 3$$

For $x-1 \leq -2$:
$$x-1 \leq -2$$
$$x \leq -1$$

So, the solution is $x \leq -1$ or $x \geq 3$.

To graph this solution on a number line, mark the points -1 and 3, and use solid dots because the inequality includes "greater than or equal to" and "less than or equal to". Then shade the regions to the left of -1 and to the right of 3 to represent the solution set.

How do you graph and solve # 3|x-1|+2&gt;=8#?

How do you graph and solve # 3|x-1|+2>=8#?