Solving Linear Inequalities: Applications and Graphing, Exercises of Pre-Calculus

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Solving Linear Inequalities

Farah Dawood

Some Application of Inequalities

Inequalities are used more often in real life than equalities:

❖ Bu sin e sse s u se in e q u a litie s to co n tro l in ve n to ry, p la n p ro d u ctio n lin e s, p ro d u ce p ricin g m o d e ls, a n d fo r sh ip p in g. ❖ Lin e a r p ro gra m m in g is a b ra n ch o f m a th e m a tics th a t u se s syste m s o f lin e a r in e q u a litie s to so lve re a l-wo rld p ro b le m s. ❖ Fin a n cia l o ccu p a tio n s o fte n re q u ire th e u se o f lin e a r in e q u a litie s su ch a s a cco u n ta n ts, a u d ito rs, b u d ge t a n a lysts a n d in su ra n ce u n d e rwrite rs to d e te rm in e p ricin g a n d se t b u d ge ts.

What is a linear Inequality?

● Linear inequality is an inequality which involves a linear function (with first power). ● Linear inequality contains one of the symbols of inequality ● The solution of a linear inequality in two variable like Ax+By>C is an ordered pair (x,y) that make an inequality true.

Solving Linear Inequalities For One Variable

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● Solve the inequality as you would an equation which

means that "whatever you do to one side, you must do to

the other side".

● If you multiply or divide by a negative number, REVERSE

the inequality symbol.

● We can write the answer in interval notation.

Example

5 - x < 4 Original Problem

5 - 5 - x < 4 - 5 -x < -1 -1 -

x > 1

Subtract 5 from BOTH sides Divide by -1 to make positive. You MUST REVERSE the SIGN since you are dividing by a negative number.

Check: 5 - x < 4 5 - 2 < 4 3 < 4

Substitute a number greater than 1, I chose

2. Since 3 is less than 4, this is a true statement and my answer is correct.

Interval Notation (1, ∞)

How to Solve and Graph a linear Inequality for Tw Variable: <><><><><><><><><><><><><><><><><><><><><><><><><><>

● Rearrange the equation so "y" is on the left and

everything else on the right.

● Plot the " y= " line (make it a solid line for y≤ or

y≥ , and a dashed line for y< or y> ).

● Shade above the line for a "greater than" ( y> or

y≥ ) or below the line for a "less than" ( y< or y≤ ).

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