Chapter ISG, Problem 5.15STP

To determine

To find J’s number

Answer to Problem 5.15STP

J’s number is 7.

Explanation of Solution

Given information:

Two inequalities are given:-

  $4x-7\ge x+14$

and

  $-x-20\le -3x-6$

Calculation:

Solving first inequality

  $4x-7\ge x+14$

On subtracting variable x on both sides

  $4x-7-x\ge x+14-x$

This gives,

  $3x-7\ge 14$

On adding 7 on both sides

  $3x-7+7\ge 21+7$

On solving,

  $3x\ge 21$

On dividing both sides by 3

  $x\ge 7$

Solving second inequality

  $-x-20\le -3x-6$

On adding 3x on both sides

  $-x-20+3x\le -3x-6+3x$

This gives

  $2x-20\le -6$

On adding 20 on both sides

  $2x-20+20\le -6+20$

On simplifying,

  $2x\le 14$

On dividing both sides by 2

  $x\le 7$

From first inequality,

  $x\ge 7$

From second inequality ,

  $x\le 7$

From both these values of ‘x’ the common value that will satisfy both the inequalities is $x=7$

Therefore J’s number is 7.