Aim: How do we solve first degree equations and inequalities? Do Now: Solve and Check

Solve for x: 1. (2x + 1) +( 4 – 3x) = 10 2. 2(x – 3) + 3(x + 4) = x + 14 3. 4x(x + 2) – x(3 + 4x) = 2x + 18

Solve and graph: 1) 2) 0 5 -6 0 6

Solve and graph reverse -3 -2

Solve and graph the inequalities. 3) 4) -6 0 -12 0

Solve and graph. 5) 6) 0 7

Interval Notation a b x b a x a b x a b x [ a, b ] a  x  b Closed [ Interval Inequality Notation Notation Line Graph Type [ a, b ] a  x  b Closed [ a, b ) a  x < b Half-open ( a, b ] a < x  b Half-open ( a, b ) a < x < b Open 1-3-5-1

Interval Notation  , , x [ b , ) x  b Closed b x ( b,  ) x > b Interval Inequality Notation Notation Line Graph Type  x [ b , ) x  b Closed b x ( b,  ) x > b b Open x –, ( a ] x  a Closed a x , , ( ( – a ) x < a Open a 1-3-5-2

Inequality Properties For a, b, and c any real numbers: 1. If a < b and b < c , then a < c . Transitive Property 2. If a < b , then a + c < b + c . Addition Property 3. If a < b , then a – c < b – c . Subtraction Property 4. If a < b and c is positive, then ca < cb . ü Multiplication Property ý (Note difference between 5. If a < b and c is negative, then ca > cb . þ 4 and 5. ) a b ü 6. If a < b and c is positive, then < . Division Property c c ý (Note difference between a b þ 6 and 7. ) 7. If a < b and c is negative, then > . c c 1-3-6