Mathematics: Equations, Inequalities, and Problem Solving
Explore the world of equations, inequalities, and problem-solving in mathematics. Learn how to solve equations by isolating variables, practice with examples, tackle word problems, and graph inequalities with step-by-step solutions. Enhance your math skills with practical applications and problem-solving strategies.
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Presentation Transcript
Unit 1 SECTION 1: SLIDES 2-6 SECTION 2: SLIDES 7-12 SECTION 3: SLIDES 13-20
Section One: Solving Equations Two expressions set equal to each other. (=) Isolate the variable. Move everything away from the variable. When moved across the = sign, do the opposite operation. Move the constant first, then the coefficient. What is an equation? How do you solve equations?
Examples x + 5 = 12 7m 17 = 60 m = 21 3x + 7 = 8
Examples y/8 + 21 = 14 19 = 3x + 7 a/7 3 = -2
Word Problems A dance academy charges $24 per class and a registration fee of $15. A student paid a total of $687, how many classes did she take? Sam has a job where he makes $12 an hour plus commission. If he made $124 in commission and his pay check was $244, how many hours did he work?
Example Find the missing variable if the perimeter is 48 inches. 2x in. 2x in. 14 in. 14 in. 8 in.
Section Two: Inequalities What is an inequality? Compares two quantities (less than, greater than) <, >, , How do you graph inequalities? Use a number line, shade the line to make the statement true
Graphing Inequalities Examples Difference between < and , open circle and closed circle. Graph: x > 5 y< 10 w 38
Solving Inequalities How do you solve inequalities? Same steps as regular equations. One difference, if you divide or multiply by a negative on the last step, flip inequality sign.
Examples 3x 7 < 8 6x 7 2x + 17 (p -12) > -2 -6y + 5 -16
Examples 5(m + 5) < 5m + 17 1 8g -4( 2g 1)
Word Problems Four more than the product of 3 and x is less than 40. Twice the sum of y and 8 is greater than or equal to -36.
Section Three: Solving equations with variables on both sides Combining like terms How do I solve an equation that has variables on both sides? Distributive property Solving
Combining Like Terms 3x + 4 = 7x 2x -12x + 9x = 24 6x
More Practice 17x - 12 - 10x + 33 2x 6 + 10 4x -x -8x + 11 + 10x 9x + x - x - 27
Distributive Property 2(x 1) + 14 2x 2(x 1) = 2(5 x)
More Practice 1 2(6x 8) + 3(x + 2) 5 (x 2) + 10x -7 8 3(x 2) + x 3 2(x + 4) - 6
Rearranging Formulas Standard Form Ax + By = C
Rearranging Formulas Slope-Intercept Form y = mx + b
Rearranging Formulas Point-Slope Form y y1 = m(x x1)
