Page 548 - Algebra 1

Example
2
Simplifying Each Side Before Solving
Solve and graph the inequality. 2(x - 8) - 3x > 6 - 3(2x + 4) SOLUTION
2(x - 8) - 3x > 6 - 3(2x + 4) 2x - 16 - 3x > 6 - 6x - 12
-x - 16 > -6x - 6 5x - 16 > -6
5x > 10 x > 2
Distributive Property Combine like terms. Add 6x to both sides. Add 16 to both sides. Divide both sides by 5.
Caution
If the operation symbol in front of the term being distributed is subtraction, multiply all the terms inside the parentheses by the opposite of the term.
Graph the inequality on a number line.
0246
Inequalities can be sometimes true, always true, or never true (false). An inequality or equation that is always true is called an identity.
A contradiction is an inequality or an equation that is never true (false).
Solving Special Cases
Determine whether each inequality is sometimes true, always true, or never true (false). If it is sometimes true, identify the solution set.
Example
3
Math Language
The solution set is
the set of values that makes an inequality true. If the inequality is a contradiction, then the solution set is empty, represented by ∅.
a. 3x+4-x>2x+7
SOLUTION
3x+4-x> 2x+7 2x + 4 > 2x + 7
Combine like terms.
Subtraction Property of Inequality
-_2_x 4>7 ✗
-_2_x
The inequality is never true (false), so it is a contradiction.
b. 3(2y-6)≤6y+4
SOLUTION
3(2y-6)≤ 6y+4 6y - 18 ≤ 6y + 4
-6y -6y __ __
Distributive Property
Subtraction Property of Inequallity
-18≤4 ✓
The inequality is always true, so it is an identity.
Lesson 81 533