When 3x+2[<5(x-4) is solved for x the solution is?

Mathematics

1 answer:

devlian [24]3 years ago

4 0

3x+2≤5(x-4)
distribute 5
3x+2≤5x-20
minus 3x both sides
2≤2x-20
add 20 both sides
22≤2x
divide by 2
11≤x
x≥11

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The given statement is which we have to prove by the principal of Mathematical Induction

$2^{n}>n$

1.→For, n=1

L H S =2

R H S=1

2>1

L H S> R H S

So,the Statement is true for , n=1.

2.⇒Let the statement is true for, n=k.

$2^{k}>k$

---------------------------------------(1)

3⇒Now, we will prove that the mathematical statement is true for, n=k+1.

$\rightarrow 2^{k+1}>k+1\\\\L H S=\rightarrow 2^{k+1}=2^{k}\times 2\\\\\text{Using 1}\\\\2^{k}>k\\\\\text{Multiplying both sides by 2}\\\\2^{k+1}>2k\\\\As, 2 k=k+k,\text{Which will be always greater than }k+1.\\\\\rightarrow 2 k>k+1\\\\\rightarrow2^{k+1}>k+1$