How do you graph and solve #3abs[s]-2 =7#?

Question

How do you graph and solve #3abs[s]-2 >=7#?

Ethan Adkins · Accepted Answer

#s<=-3, s>=3# See below for graph details:

Let's isolate #s#: #3abss-2>=7# #3abss>=9# #abss>=3# It's at this point that it's important to remember that the absolute value function will only return positive values (but the #s# inside of it could be negative). And so we evaluate for both positive and negative values: #pms>=3# Positive #s>=3# Negative #-s>=3# #s<=-3# Now to graph. On a number line, put filled in dots on #3 and -3# - this indicates that these values are part of the solution. Draw a ray to the right from the 3 dot and a ray to the left for the #-3# dot.

Ethan Adkins · Answer

undefined To graph and solve the inequality $3|s| - 2 \geq 7$, you can follow these steps:

1. Add 2 to both sides of the inequality to isolate the absolute value term: $3|s| \geq 9$.
2. Divide both sides by 3 to isolate the absolute value term: $|s| \geq 3$.
3. Consider two cases: $s$ is either greater than or equal to 3, or $s$ is less than or equal to -3.
4. Graph the two cases separately on a number line, marking the points where $s$ equals 3 and -3 with solid circles to indicate inclusion in the solution set.
5. Shade the regions where $s$ is greater than or equal to 3, and where $s$ is less than or equal to -3, to represent the solution set on the number line.
6. The solution to the inequality is the union of the shaded regions on the number line, which indicates all values of $s$ that satisfy the inequality.

How do you graph and solve #3abs[s]-2 &gt;=7#?

How do you graph and solve #3abs[s]-2 >=7#?