Solve the following inequality algebraically. x +14x +40 <0

Mary Jackson

Mary Jackson

Answered question

2021-12-14

Solve the following inequality algebraically. x+14x+40<0

Answer & Explanation

Paul Mitchell

Paul Mitchell

Beginner2021-12-15Added 40 answers

Step 1
Here the given inequality is
x2+14x+400 (1)
Step 2
Let us factorize x^{2}+14x+40
x2+14x+40
x2+10x+4x+40
x(x+10)+4(x+10)
(x+10)(x+4) (2)
From (1) and (2) we get
(x+10)(x+4)0 (3)
From (3) we get, either
x+100 and x+40

x10 and x4, which is impossible.
Or, from (3) we get
x+100 and x+40
x10 and x4
x[10,4]
So, the required answer will be x[10,4].

Becky Harrison

Becky Harrison

Beginner2021-12-16Added 40 answers

Step 1
To solve the inequality algebrically
x2+14x+400
Step 2
Given that
x2+14x+400
x2+10x+4x+400
x(x+10)+4(x+10)0
(x+10)(x+4)0
x+100 or x+40
x10 or x4
Hence x[10,4]

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