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denpristay [2]
3 years ago
13

Explain why the following expression is false. |x| < -4

Mathematics
1 answer:
levacccp [35]3 years ago
8 0

Step-by-step explanation:

Whenever we put a negative number inside a modulus function it will give us the positive output. For example , |-3| = 3 , |-6|=6, |5|= 5 ,etc.

So a modulus function i.e. |x| is always greater than zero ( positive ) when x is any number except 0 and it is equal to zero when the value of x is 0.

So |x| can't be less than -4 as |x| is always positive . So the statement is false.

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2.\ x^2+14x+49=0\\\\x^2+2x\cdot7+7^2=0\\\\(x+7)^2=0\\\\(x+7)(x+7)=0\iff x=-7

3.\ x^2-17x+42=0\\\\x^2-14x-3x+42=0\\\\x(x-14)-3(x-14)=0\\\\(x-14)(x-3)=0\iff x=14\ \vee\ x=3

4.\ 2x^2-9x-5=0\\\\2x^2-10x+x-5=0\\\\2x(x-5)+1(x-5)=0\\\\(x-5)(2x+1)=0\iffx=5\ \vee\ x=-\frac{1}{2}

5.\ 3x^2+11x-4=0\\\\3x^2+12x-x-4=0\\\\3x(x+4)-1(x+4)=0\\\\(x+4)(3x-1)=0\iff x=-4\ \vee\ x=\frac{1}{3}

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