1. Warm-up 9/6 Write the STANDARD FORM equation of the line that passes
through (4, -5) with a slope of ½ .
2. Solve: 2x – 5 = 7
3. Solve: 2x – 5 ≥7

2. Solving Inequalities REMEMBER:
Objectives:
To solve and graph inequalities.
To solve and write compound inequalities.
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Solutions of inequalities are numbers that make them true. Unlike equations, there are often many solutions. The properties of inequalities are similar to equations, with ONE exception…
Equation Inequality
-6x = x > 24
REMEMBER:
X < # …………………………………………………… open circle on number, shade left
X ≤ # …………………………………………………… closed circle on number, shade left
X > # …………………………………………………… open circle on number, shade right
X ≥# …………………………………………………… closed circle on number, shade right

3. When you multiply or divide both sides of an inequality, you must REVERSE the inequality symbol.
Ex) Solve and Graph the following.
3x – 6 < – 5x < 21
12 > 2(3n + 1) ( x + 3) ≥ 7 ( x – 1)

4. Some inequalities have no solution, and some are true for all real numbers.
Ex) No Solutions or All Real Numbers as Solutions
2x < 2(x + 1) (x – 3) + 7 > 4x + 1

5. A salesperson earns a salary of $700 per month plus 2% of the sales
A salesperson earns a salary of $700 per month plus 2% of the sales. What must the sales be if the salesperson is to have a monthly income of at least $1800?

6. COMPOUND INEQUALITIES
Definition: a pair of inequalities joined by and or or.
“and” – find all values that make BOTH true.
(i.e. the “overlap” in the two inequalities is the solution to the
compound inequality)
“or” - find values that make EITHER true.
(i.e. both solution sets satisfy the compound inequality)
Ex) Graph the solutions.
2x > x AND x – 7 < 2
x – 1 < 3 OR x + 3 > 8

7. “And” problems can be written TWO ways….
Ex) Solve:
3 < x + 1 ≤ 5 m – 2 ≥ 5 and m + 4 ≤ -2

8. Write the equation of the compound inequalities shown: