Question

Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 2p − 8 < 5p + 4 true.

Answer 1

Answer:

s:[-2,-3] is the answer

Answer 2

The set S:{ - 2 , - 3 } will make the inequality 2p - 8 < 5p + 4 true

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

The set S : { - 2 , - 3 , - 4 , - 5 }

The inequality relation is 2p - 8 < 5p + 4

Now , substituting the value from set S in the inequality , we get

When p = - 2 :

2p − 8 < 5p + 4

2(-2) − 8 < 5(-2) + 4

-4 − 8 < -10 + 4

-12 < -6  TRUE

When p = - 3

2p − 8 < 5p + 4

2(-3) − 8 < 5(-3) + 4

-6 − 8 < -15 + 4

-14 < -11  TRUE

When p = - 4

2p − 8 < 5p + 4

2(-4) − 8 < 5(-4) + 4

-8 − 8 < -20 + 4

-16 < -16  FALSE

When p = - 5

2p − 8 < 5p + 4

2(-5) − 8 < 5(-5) + 4

-10 − 8 < -25 + 4

-18 < -21  FALSE

Therefore , the value of p = - 2 , - 3 will satisfy the given inequality relation

Hence , the set S:{ -2,-3 } is the solution

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