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Questions  >>  CBSE XI  >>  Math  >>  Linear Inequalities

A man wants to cut three length from a single piece of board of length 91 cm . The second length is to be 3 cm longer than the shortest , and third length is to be twice as long as shortest. What are the possible lengths of the shortest board, if the third piece is to be at least 5 cm longer than the second.

1 Answer

  • Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
  • Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
  • If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $ '>'$ sign changes to $'<' $ and $'<'$ changes $'>'$ .
Let the length of the shortest piece, The length of the second price is $(x+3)$cm. The length of the third piece is 2x cm, Total length of the three prieces must be $\leq 91 cm$.
$x cm +(x+3) cm +2x cm \leq 91\;cm$
$=> 4x +3 \leq 91$
Subtracting 3 from number 4 on both sides, $ \large\frac{4x}{4} \leq \frac{88}{4}$
$x \leq 22$----(1)
Step 2:
Also third piece is at least 5 cm longer than the second piece. therefore
$2x \geq (x+3) +5$
$=> 2x \geq x+8$
Subtracting x from both sides,
$2x -x \geq 8$
$ x \geq 8$ -----(2)
Step 3:
From (1) and (2)
$8 \leq x \leq 22$
The possible length of the shortest side must be greater than or equal to 8 cm and less than or equal to 22 cm.
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