Question 56

If 5x - 3 ≥ 3 + x/2 and 4x - 2 ≤ 6 + x; then x can take which of the following values?

Solution

Expression 1 : 5x - 3 ≥ 3 + x/2

=> $$5x-\frac{x}{2} \geq 3+3$$

=> $$\frac{9x}{2} \geq 6$$

=> $$x \geq \frac{4}{3}$$ ------------(i)

Expression 2 : 4x - 2 ≤ 6 + x

=> $$4x-x \leq 6+2$$

=> $$3x \leq 8$$

=> $$x \leq \frac{8}{3}$$ ------------(ii)

Combining inequalities (i) and (ii), we get : $$\frac{4}{3} \leq x \leq \frac{8}{3}$$

The only value that $$x$$ can take among the given options = 2

=> Ans - (B)

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If 5x ­- 3 ≥ 3 + x/2 and 4x -­ 2 ≤ 6 + x; then x can take which of the following values?