Question

Solve the inequality and write your answer in interval notation.
0.1x+0.8≤13.8+0.7x

Answer 1

you could add -0.1x to both sides.
what do you get ?

Answer 2

multiplie both sides by 10 for you c

Answer 3

can eliminate the decimals

Answer 4

with integers you can calculi more easy

Answer 5

ditto

so... how would "you" solve ... say 0.1x+0.8 = 13.8+0.7x ?

Answer 6

0.1x+0.8≤13.8+0.7x
0.8<=13.8+.6x
-13<=0.6x

Answer 7

12.67=x?

Answer 8

how do i write it in interval notation?

Answer 9

12.67... actually close
but yes, you'd do the same more or less, as you'd do in an equation

Answer 10

\(\bf 0.1x+0.8\le13.8+0.7x\implies 0.8\le 13.8+0.6x
\\ \quad \\
-13\le 0.6x\implies \cfrac{-13}{0.6}\le x\)

Answer 11

the only difference is that, in inequalities, when you multiply or divide or exponentialize by a negative number, you have to "flip" the inequality sign

notice above, we divided by 0.6, BUT 0.6 is positive, so the sign remains \(\large \le\)

Answer 12

to use decimals
-13/0.6 is -21.6666
so, the inequaliy is saying
"x" is a value that greater than or equals to -21.6666
recall that
on the negative side, the closer to the 0, the bigger the number
so -19 is bigger than -21, because -19 is closer to the 0

so, interval notation wise