Equations and Inequalities

Equation – A sentence stating that two qualities are equal. Includes a variable – 3x + 5 = 17 Equation variable The solution is the value that makes the equation true. When graphed the point falls on the line. equivalent equations have the same value. unknown value

FIRST – replace the variables with the known (given) value. THEN – follow the Order of Operations. EX1) Determine if -1, 0, 1 are solutions to the equations 3X + 2 = 5 3(-1) + 2 = = 5 ? no 3(0) + 2 = = 5 ? no 3(1) + 2 = = 5 ? yes = = 1.2 ? no = = 1.2 ? yes = = 1.2 ? no EX2) Determine if 1.2, 1.4, 2.6 are solutions to the equations = 1.2 x

Inequalities – a mathematical sentence that compares quantities ˂ ˃ Comparison Symbols ˃ ˂ Less Than Greater Than Less Than or equal to Greater Than or equal to 3x ˂

Determine if -3, 5, 8 are solutions to the equations 2 - 3x > > -13 ? yes > -13 ? no > -13 ? no > -13 ? ? ? 2 - 3(5) > -13 ? 2 - 3(8) > -13 ? 2 - 3(-3) > -13 ? EX3)

Determine if - 24, 12, 28 are solutions to the inequality no EX4) x < 3 ? < 3 ? 14 < 3 ? < 3 ? yes < 3 ? 3 ? ? yes < 3 ? < 3 ? ?

Essential Question How do you know whether a value is a solution to an equation?

Equations and Inequalities Date ____________

Equation – Includes a _______ – 3x + 5 = 17 The ______________ is the value that makes the equation true. When graphed the point falls ___ _____ ______. _________________ have the same value.

FIRST – replace the variables with the known (given) value. THEN – follow the Order of Operations. EX1) Determine if -1, 0, 1 are solutions to the equations EX2) Determine if 1.2, 1.4, 2.6 are solutions to the equations

Inequalities – a mathematical sentence that compares quantities ˂ ˃ Comparison Symbols ˃ ˂

Determine if -3, 5, 8 are solutions to the equations EX3)

Determine if - 24, 12, 28 are solutions to the inequality EX4)

Essential Question How do you know whether a value is a solution to an equation?