Question

Which is the solution set to the given inequality |x+3|<12? x infinity(-15,9), x infinity {-15,9], x infinity (00,-15)U(9,00), x infinity (-00,-15)n(9,00)
Which ordered pair is a solution to the system?
{y>-2
{x + y less than or equal to 4

(1,5)
(0,5)
(-2,-3)
(1,3)

I really need help I am failing algebra II and just can't seem to understand it or graphing

Answer 1

Answer:

Part 1) The solution set is (-15,∞) ∩ (-∞,9)=(-15,9)

Part 2) The ordered pair (1,3) is a solution of the system

Step-by-step explanation:

Part 1) we have

$\left|x+3\right|$

First solution case Positive

$+(x+3)$

$x$

$x$

The solution first case is the interval -------> (-∞,9)

Second solution case Negative

$-(x+3)$

$-x-3$

$-x$

$-x$ ------> Multiply by -1 both sides

$x>-15$

The solution second case is the interval -------> (-15,∞)

The solution set is equal to

(-15,∞) ∩ (-∞,9)=(-15,9)  

Part 2) we have

$y>-2$ -------> inequality A

$x+y\leq 4$ -----> inequality B

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

Verify each case

case a) (1,5)

Substitute the value of x and the value of y in the inequality and then compare

Inequality A

$5>-2$ ------> is true

Inequality B

$1+5\leq 4$

$6\leq 4$ -----> is not true

therefore

the ordered pair is not a solution

case b) (0,5)

Substitute the value of x and the value of y in the inequality and then compare

Inequality A

$5>-2$ ------> is true

Inequality B

$0+5\leq 4$

$5\leq 4$ -----> is not true

therefore

the ordered pair is not a solution

case c) (-2,-3)

Substitute the value of x and the value of y in the inequality and then compare

Inequality A

$-3>-2$ ------> is not true

therefore

the ordered pair is not a solution

case d) (1,3)

Substitute the value of x and the value of y in the inequality and then compare

Inequality A

$3>-2$ ------> is true

Inequality B

$1+3\leq 4$

$4\leq 4$ -----> is true

therefore

the ordered pair is  a solution