Question

The solution set for all real numbers x such that 2x + 3 < 19 and 2x − 3 ≤ -7 is (, ).

Note: If needed, type “-infinity” for -∞ and “infinity” for ∞.

Answer 1

@jim_thompson5910

Answer 2

first just focus on solving 2x + 3 < 19 (ignore the other inequality)

Answer 3

Alright.

Answer 4

When x= anything negitive wouldn't it be less than 19?

Answer 5

how would you solve something like 2x+3 = 19 ?

Answer 6

I'd solve it by pluging in numbers for X?

Answer 7

so a guess and check method?

Answer 8

Practically, yes.

Answer 9

that might take a while, why not subtract 3 from both sides

2x+3 = 19
2x+3-3 = 19-3
2x+0 = 16
2x = 16

then divide both sides by 2

2x = 16
2x/2 = 16/2
x = 8

Answer 10

To solve equations, you follow PEMDAS in reverse and undo everything to isolate the variable you want

Answer 11

when I subtracted 3 from both sides, I did that to undo the +3

when I divided both sides by 2, I undid the multiplication of 2

Answer 12

I seen that, So then X would just equal 8? Nothing less?

Answer 13

well that's the equation form

Answer 14

we're dealing with inequalities though

Answer 15

use the same steps to solve 2x+3 < 19


2x+3 < 19
2x+3-3 < 19-3
2x < 16
2x/2 < 16/2
x < 8


make sense?

Answer 16

It does. Since pluging 8 in as x would cause it to be 19 we need less than 19.

Answer 17

solve 2x − 3 ≤ -7 and tell me what you get

Answer 18

X=-2

Answer 19

it's not an equation though

Answer 20

you should get \(\Large x \le -2\)

Answer 21

Ah. My bad.

Answer 22

so solving the two inequalities
2x + 3 < 19 and 2x − 3 ≤ -7
leads to
x < 8 and x ≤ -2

Answer 23

the keyword "and" is very important here

Answer 24

think of a number that is BOTH smaller than 8 AND less than or equal to -2

what number do you come up with?

Answer 25

Well, that could be anything beyond -2 could it not?

Answer 26

Let's use a number line

Answer 27

the graph of x < 8 would look like this



it has an open hole at 8 and the shading is to the left