How do you solve and graph #f-6=2#?

Question

How do you solve and graph #f-6<5# and #f-4>=2#?

Eva Abramson · Accepted Answer

Mathematically, this is expressed as #6<=f<11#

We first need to solve each part of this problem:

#f-6<5=>f<11#

#f-4>=2=>f>=6#

The graph, then, will consist of a line along the #f#-axis (probably looking very much like a number line) and will be a solid dot at 6 (to indicate that 6 is part of the solution), a hollow dot at 11 (to indicate that all the points up to but not including 11 are part of the solution), and a solid line connecting the two dots.

Mathematically, this is expressed as #6<=f<11#

Jace Anderson · Answer

undefined To solve the compound inequality f - 6 < 5 and f - 4 ≥ 2, you would first solve each inequality separately, and then find the intersection of their solution sets.

1. For the inequality f - 6 < 5:
   Add 6 to both sides: f < 11.

2. For the inequality f - 4 ≥ 2:
   Add 4 to both sides: f ≥ 6.

So, the solutions for the compound inequality are 6 ≤ f < 11.

To graph this on a number line, you would draw a closed circle at 6 (since it includes 6) and an open circle at 11 (since it does not include 11), and then shade the area in between the two circles to represent the values of f that satisfy both inequalities.

How do you solve and graph #f-6&lt;5# and #f-4&gt;=2#?

How do you solve and graph #f-6<5# and #f-4>=2#?