Transcript 1.6 – Solve Linear Inequalities

1.6 – Solve Linear Inequalities
A linear inequality in one variable can be
written in one of the following forms, where a
and b are real numbers and a does not
equal 0.
A solution of an inequality in one variable is a
value that, when substituted for the variable,
results in a true statement. The graph of an
inequality in one variable consists of all points
on a number line that represent solutions.
1.6 – Solve Linear Inequalities
Example 1:
a. Graph x < 2.
b. Graph x > -1
1.6 – Solve Linear Inequalities
Compound Inequalities:
A compound inequality consists of two simple
inequalities joined by “and” or “or”.
1.6 – Solve Linear Inequalities
Example 2
a. Graph -1 < x < 2
b. Graph x < -2 or x > 1.
1.6 – Solve Linear Inequalities
Solving Inequalities:
To solve a linear inequality in one variable, you
isolate the variable using transformations
that produce equivalent inequalities, which
are inequalities that have the same
solutions as the original inequality.
1.6 – Solve Linear Inequalities
Example 3
You have $50 to spend at a county fair. You
spend $20 for admission. You want to play
a game that costs $1.50. Describe the
possible number of times you can play the
game.
1.6 – Solve Linear Inequalities
Example 4
Solve 5x + 2 > 7x – 4
1.6 – Solve Linear Inequalities
Example 5
Solve -4 < 6x – 10 < 14
1.6 – Solve Linear Inequalities
Example 6
Solve 3x + 5 < 11 or 5x – 7 > 23 .