Question

Solve inequality and write the solution set using both set-builder
notation and interval notation.

Answer 1

\[-3a-15\le-2a+6\]

Answer 2

\[-21 \le a\]\[[-21,\infty)\]

Answer 3

how?

Answer 4

\[-3a-15 \le -2a+6\]add 3a and subtract 6 from both sides:\[-15-6 \le-2a+3a\]\[-21 \le a\]

Answer 5

for instance how would i do the same for another like this one that is harder

\[-8(-2x+3)+6(4+5x)\ge-2(1-7x)-4(4-6x)\]

Answer 6

just like a regular equation, combine like terms and isolate the variable.

Answer 7

ahh ok like terms.
set-builder
notation and interval notation threw me off

Answer 8

do you understand why\[-21 \le a\]is written as\[[-21,\infty)\]in interval notation?

Answer 9

how would we do one like this... do we just move to both sides?

\[-2(-2x-13)\ge2(1-3x)-5(4+2x)\ge4(x-3)\]

Answer 10

-21 is less than a number so wouldnt it go to neg infin?

Answer 11

oh wait read that wrong
a number is larger than -21

Answer 12

did you delete that?

Answer 13

I messed up earlier, let me try again...

Answer 14

ok

Answer 15

well we have to get rid of those parentheses first, so
4x+26≥2−6x−20-10x≥4x−12
4x+26≥-16x−18≥4x−12

let's try to get x into the middle of this expression, so subtract 4x from everywhere:\[26 \ge-20x-18 \ge -12\]add 18 everywhere:\[44 \ge -20x \ge6\]nowe to isolate x we must divide by -20, which means we have to turn all the inequalities around, so:\[-11/5 \le x \le-3/10\] in interval notation\[[-11/5,-3/10]\]
as to your other question, yes a is greater-then or equal-to -21, so it goes to positive infinity

Answer 16

The trick with the problems with two inequality symbols is to try to isolate x and get it into the middle of the expression so that we can say "x is between a and b"
in math we write this as
a<x<b or (a,b) or {x:a<x<b}
(above is expression, interval notation, set builder notation)

Answer 17

−2(−2x−13)≥2(1−3x)−5(4+2x)≥4(x−3)

well we have to get rid of those parentheses first, so

4x+26≥2−6x−20-10x≥4x−12
4x+26≥-16x−18≥4x−12

let's try to get x into the middle of this expression, so subtract 4x from everywhere:

26≥−20x−18≥−12

add 18 everywhere:

44≥−20x≥6

nowe to isolate x we must divide by -20, which means we have to turn all the inequalities around, so:

−11/5≤x≤−3/10

in interval notation:

[−11/5,−3/10]

I rewrote the whole thing together for the sake of completeness.

Answer 18

but i would have to find the set builder notation as well do i?

Answer 19

{x:-11/5<x<-3/10} is how I know to write this in set-builder notation, but I've also seen it written as\[x \in \left\{ x:-11/5\le x \le-3/10 \right\}\]

Answer 20

ok ill write it your way looks more like we write in class

Answer 21

quick question... how would i write the first equation as a set builder notation?

Answer 22

[−21,∞) in set-builder is\[\left\{ x:x \ge-21 \right\}\]