Can you solve and give me explanation how to solve

9514 1404 393

  3 < x < 6

Step-by-step explanation:

Use the perimeter formula to write an expression for the perimeter. Then put that in an inequality with the given limits. Solve for x.

  P = 2(L +W)

  P = 2((4x) +(2x +1)) = 2(6x +1) = 12x +2 . . . . . fill in the given values; simplify

The perimeter wants to be between 38 and 74 cm, so we have ...

  38 < 12x +2 < 74

  36 < 12x < 72 . . . . . subtract 2

  3 < x < 6 . . . . . . . . . divide by 6

Additional comment

Solving a compound inequality is very much like solving a single inequality. You need to "undo" what is done to the variable. The rules of equality (ordering) still apply. If you were to multiply or divide by a negative number, the direction (sense) of the inequality symbols would reverse in the same way they do for a single inequality.

Here, our first step was to subtract 2 from all parts of the inequality:

  38 -2 < 12x +2 -2 < 74 -2   ⇒   36 < 12x < 72

The division by 12 worked the same way: all parts are divided by 12.

  36/12 < (12x)/12 < 72/12   ⇒   3 < x < 6

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If it makes you more comfortable, you can treat the perimeter limits as two separate inequalities: 38 < 12x+2 and 12x+2 < 74. Both restrictions apply, so the solution set is the intersection of the solution sets of these separate inequalities.

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