Chapter ISG, Problem 5.4.1.9P

a.

To determine

To write compound inequality equation.

Answer to Problem 5.4.1.9P

Compound inequality is $5+x>14-(5-x)$ or $x+(5+x)>5$ or $(5+x)+5>x$

Explanation of Solution

Given information:

  

One side is 5 m long

Unknown side is x

Perimeter is 14 m

Formula used:

Perimeter of triangle,

  $P=a+b+c$

Where a, b and c are sides of triangle

Calculation:

a=5

b=x

c= unknown

Substituting value of a, b and c in the formula,

  $P=5+x+unknown$

Substituting the value of perimeter,

  $14=5+x+unknown$

Shifting left-hand side values to right hand side,

  $unknown=14-(5+x)$

For Compound inequality,

  $5+x>14-(5-x)$

Or

  $x+(5+x)>5$

Or

  $(5+x)+5>x$

Hence, compound inequality is $5+x>14-(5-x)$ or $x+(5+x)>5$ or $(5+x)+5>x$

b.

To determine

To explain about two unknown sides.

Answer to Problem 5.4.1.9P

The unknown side is $7<x<9$

Explanation of Solution

Given information:

Compound inequality is $5+x>14-(5-x)$ or $x+(5+x)>5$ or $(5+x)+5>x$

Formula used:

Perimeter of triangle,

  $P=a+b+c$

Where a, b and c are sides of triangle

Calculation:

For inequality1,

  $5+x>14-(5-x)$

Opening brackets,

  $5+x>14-5-x$

On solving,

  $5+x>9-x$

Shifting values,

  $x+x>9-5$

On solving,

  $2x>4$

Cross-multiplying,

  $x>2$

For inequality 2,

  $x+5+x>5$

On solving,

  $2x+5>5$

Shifting the values,

  $2x>5-5$

On solving,

  $2x>0$

Cross multiplying,

  $x>0$

For inequality 3,

  $5+x+5>x$

On solving,

  $10+x>x$

Shifting values,

  $10>x-x$

On solving,

  $10>0$

When x=2

Then, unknown side= $9-2$ ,

On solving,

  $unknown=7$

When x=0

Then, unknown side= $9-2$

On solving,

  $unknown=9$

Hence, the unknown side,

  $7<x<9$