Question

Solve the inequality and show on a number line

(picture included below)

Answer 1

Step-by-step explanation:

I cant show a number line so i'll do my best to explain how its graphed.

15) x - 1 < 15

add 1 to both sides:

x < 16

Because it is less than, rather than less than or equal to, it's graphed with an open circle (not filled in) on 16, and everything less than 16 highlighted

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16) 2(y + 1) - 2 ≥ 12

distribute the 2:

2y + 2 - 2 ≥ 12

combine like terms

2y ≥ 12

isolate y:

y ≥ 6

This one is greater than or equal to, so it's graphed with a closed circle (filled in) and everything above 6 highlighted

Answer 2

15

$x-1<15$

Add 1 to both sides:

$x<16$

On a number line, you should highlight all numbers to the left of 16, excluded.

16

$2(y+1)-2\geq 12$

Expand the left hand side:

$2y+2-2\geq 12$

Sum like terms on the left hand side:

$2y\geq 12$

Divide both sides by 2:

$y\geq 6$

On a number line, you should highlight all numbers to the right of 6, included.