Needed solve for p. 2p+5> 2(p−3) no solution all real numbers p> −9 p> −3 what is the solution to the compound inequality in interval notation? 4(x+1)> −4  or  2x−4≤−10 (−∞, −3] or (2, ∞) (−3, −2] (−∞, −2) or [3, ∞) (−∞, −3] or (−2, ∞)

First problem:

2p + 5 > 2(p − 3)

Distribute 2.

2p + 5 > 2p - 6

Subtract 2p from both sides.

5 > -6

Since 5 > -6 is a true statement, the inequality is true for all real numbers.

all real numbers.

Second problem:


4(x + 1) > −4  or  2x − 4 ≤ −10

Distribute 4.

4x + 4 > -4 or 2x - 4 ≤ −10

Subtract 4 from both sides in left inequality.
Add 4 to both sides in right inequality.

4x > -8 or 2x ≤ −6

Divide both sides of left inequality by 4.
Divide both sides of right inequality by 2.


x > -2 or x ≤ −3

x is greater than -2, so we start the interval at 2, but not including 2, so we use a left parenthesis symbol. The interval goes to positive infinity.
x is less than or equal to -3, so -3 is included in the interval, so we use a right square bracket to include the -3. We start this interval at negative infinity.

(-∞, -3] or (-2, ∞)

Notice that with infinity and negative infinity we always use a regular parenthesis, not a square bracket.