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# Alg 2 - 1.1 Solve and Graph Linear Inequalities

Solve and Graph Linear Inequalities

by

Tweet## Benjamin Lawrence

on 9 September 2010#### Transcript of Alg 2 - 1.1 Solve and Graph Linear Inequalities

Solve and Graph Linear Inequalities Solving Inequalities Graph Linear Inequalities Same process as linear equations except... The direction of the inequality changes

when we multiply or divide by a negative number. Examples As a Group "x is greater than or equal to 5" "x is less than negative 7" Important symbols "<" is less than ">" is greater than "≤" is less than or equal to "≥" is greater than or equal to Once the inequality has been algebraically

solved, it is now time to graphically solve

the inequality. Draw a horizontal number line In which direction are "greater" numbers? And lesser numbers are to the... left. Strict inequalities are

not equal to (< and >) Use an open circle The other two types of inequalities

(≤ and ≥) Use a closed circle Examples Graph the solutions

to 1.1.1 and 1.1.2 Write the following problems as algebraic inequalities, then solve and graph them.

1.1.6

Two more than a number is less than ten.

1.1.7

A quarter of three less than a number is at least fifteen. 1.1.6

x + 2 < 10

x < 8

1.1.7

1.1.8

Five fewer than a value is greater than seven.

1.1.9

Three times a number is at most

thirty-seven.

1.1.10

Twice a number is less than twelve

more than half the number.

x ≥ 63 The value of x is less than eight.

The value of x is greater than or equal to 63. 1.1.11

A number is at least eight more than three times itself.

1.1.12

Seven less than two-thirds of a number is greater than two more than half of the same number. x - 5 > 7

Full transcriptwhen we multiply or divide by a negative number. Examples As a Group "x is greater than or equal to 5" "x is less than negative 7" Important symbols "<" is less than ">" is greater than "≤" is less than or equal to "≥" is greater than or equal to Once the inequality has been algebraically

solved, it is now time to graphically solve

the inequality. Draw a horizontal number line In which direction are "greater" numbers? And lesser numbers are to the... left. Strict inequalities are

not equal to (< and >) Use an open circle The other two types of inequalities

(≤ and ≥) Use a closed circle Examples Graph the solutions

to 1.1.1 and 1.1.2 Write the following problems as algebraic inequalities, then solve and graph them.

1.1.6

Two more than a number is less than ten.

1.1.7

A quarter of three less than a number is at least fifteen. 1.1.6

x + 2 < 10

x < 8

1.1.7

1.1.8

Five fewer than a value is greater than seven.

1.1.9

Three times a number is at most

thirty-seven.

1.1.10

Twice a number is less than twelve

more than half the number.

x ≥ 63 The value of x is less than eight.

The value of x is greater than or equal to 63. 1.1.11

A number is at least eight more than three times itself.

1.1.12

Seven less than two-thirds of a number is greater than two more than half of the same number. x - 5 > 7