Question

if 3 is added to 2 times of a whole number is less than 11. Show in it inequality and solve it​..



plz help me to solve this question step by step

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that whole number be x.

According to statement,

if 3 is added to 2 times of a whole number is less than 11.

So,

$\rm :\longmapsto\:3 + 2x < 11$

On Subtracting 3, from both sides, we get

$\rm :\longmapsto\:3 + 2x - 3 < 11 - 3$

$\rm :\longmapsto\:2x < 8$

$\rm :\longmapsto\:x < 4$

As x is a whole number,

Therefore,

$\rm :\longmapsto\:x \: \in \: \{0, \: 1, \: 2, \: 3 \}$

Additional Information :-

Example :-

An integer is such that one third of the next integer is atleast 2 more than one fourth of the previous integer. Express it in inequality and hence solve it.

Solution :-

Let the integer be x.

According to statement,

One third of the next integer is atleast 2 more than one fourth of the previous integer.

$\rm :\longmapsto\:\dfrac{x + 1}{3} \geqslant \dfrac{x - 1}{4} + 2$

$\rm :\longmapsto\:\dfrac{x + 1}{3} \geqslant \dfrac{x - 1 + 8}{4}$

$\rm :\longmapsto\:\dfrac{x + 1}{3} \geqslant \dfrac{x + 7}{4}$

$\rm :\longmapsto\:4x + 4 \geqslant 3x + 21$

$\rm :\longmapsto\:4x - 3x \geqslant \: 21 - 4$

$\rm :\longmapsto\:x \geqslant \: 17$

$\bf\implies \:x \: \in \: [17, \: \infty )$

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