Question

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Answer 1

Question:-

Solve the inequation:-

(2x – 1)/3 < 5/2

Answer:-

• The solution set is {0,1,2,3,4}.

Solution:-

$\large{ \tt : \implies \: \: \: \: \frac{2x - 1}{3} \leqslant 2 \times \frac{1}{2} }$

$\large{ \tt : \implies \: \: \: \: \frac{2x - 1}{3} \leqslant \frac{5}{2} }$

$\large{ \tt : \implies \: \: \: \: \frac{(2x - 1)}{ \cancel3} \times \cancel3 \leqslant \frac{5}{2} \times 3}$

$\large{ \tt : \implies \: \: \: \: 2x \cancel{ - 1} \cancel{+ 1 }\leqslant \frac{15}{2} + 1}$

$\large{ \tt : \implies \: \: \: \: 2x \leqslant \frac{15 + 2}{2} }$

$\large{ \tt : \implies \: \: \: \: \frac{2x}{2} \leqslant \frac{17}{2 \times 2} }$

$\large{ \tt : \implies \: \: \: \: x \leqslant \frac{17}{4} }$

$\large{ \tt : \implies \: \: \: \: x \leqslant 4.25}$

It is evident that 0,1,2,3,4 are the only whole numbers less or equal to 4.25

Thus,

When x is a whole number ,the solutions of the given inequality are 0,1,2,3,4

Hence,

The solution set is {0,1,2,3,4}.

Answer 2

Let's solve your equation step-by-step.

$\dfrac{2x-1}{3}\leq 2\dfrac{1}{2}$

Step 1: Simplify the equation.

⇒ $\dfrac{2x-1}{3}\leq 2\dfrac{1}{2}$

⇒ $\dfrac{2}{3}x + \dfrac{-1}{3} \leq 2\dfrac{1}{2}$

Step 2: Add $\frac{1}{3}$ to both sides of the equation.

⇒ $\dfrac{2}{3}x + \dfrac{-1}{3} +\dfrac{1}{3} \leq 2\dfrac{1}{2}+\dfrac{1}{3}$

⇒ $\dfrac{2}{3}x \leq \dfrac{5}{2} +\dfrac{1}{3}$

⇒ $\dfrac{2}{3}x \leq \dfrac{5\times 3 }{2\times 3 } +\dfrac{1\times 2}{3\times 2}$

⇒ $\dfrac{2}{3}x \leq \dfrac{15}{6} +\dfrac{2}{6}$

⇒ $\dfrac{2}{3}x \leq \dfrac{17}{6}$

Step 3: Multiply both sides by $\frac{3}{2}$.

⇒ $\dfrac{3}{2} \times \dfrac{2}{3}x \leq \dfrac{3}{2} \times \dfrac{17}{6}$

⇒ $x \leq \dfrac{17}{4}$

⇒ $x \leq 4.25$

∴ The possible numbers for the value of 'x' would be any number below 4.25

∴ It could 0, 1, 2, 3, 4, etc.

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