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© Mr. Sims Algebra 1 Section 1.5 Equations and Inequalities Equation - is formed when an equal sign is placed between two algebraic expressions Examples: x–2=3 3x = 27 5x – 6 = x2 + 8 To check an equation, substitute the possible solution into the equation for the variable. If the resulting statement is true, then the number substituted in is a solution to the equation. For example: Check whether the numbers 2, 3, and 4 are solutions to the equation 3x – 1 = 11. x 2 3 4 substitution 3(2) – 1 = 11 3(3) – 1 = 11 3(4) – 1 = 11 conclusion 2 is not a solution 3 is not a solution 4 is a solution © Mr. Sims Check whether the given number is a solution to the equation. 1. 3x + 1 = 13, 4 3(4) + 1 = 13 12 + 1 = 13 13 = 13 yes 4 is a solution 2. 4y + 2 = 2y + 8, 3 4(3) + 2 = 2(3) + 8 12 + 2 = 6 + 8 14 = 14 yes 3 is a solution 3. 5x – 2 = 11, 2 5(2) – 2 = 11 10 – 2 = 11 8 11 no 2 is not a solution 4. x3 = 27, 2 23 = 27 8 27 no 2 is not a solution © Mr. Sims Inequality - is formed when an inequality symbol is placed between two algebraic expressions. Examples: 3x + 2 8 2x < 10 x2 > 6 Inequality Symbol < > Meaning is less than is greater than is less than or equal to is greater than or equal to Check whether the given number is a solution to the inequality. 6. 6 + 2x 10, 2 5. x – 2 < 6, 7 6 + 2(2) 10 7–2<6 6 + 4 10 5<6 10 10 yes yes 7 is a solution 2 is a solution to to the inequality the inequality © Mr. Sims 7. 4x – 3 <0, 1 4(1) – 3 <0 4 – 3 <0 1 <0 no 1 is not a solution to the inequality 8. 2x2 – 3 15, 2 2(2)2 – 3 2(4)– 3 15 8 – 3 5 no 2 is not a solution to the inequality © Mr. Sims Check whether the given number is a solution to the equation or inequality. 9. x2 – 10 > 16 , 6 62 – 10 > 16 36 – 10 > 16 26 > 16 yes 6 is a solution to the inequality 10. 10 x 12 , 14 7 10 14 12 7 10 + 2 = 12 12 = 12 yes 14 is a solution to the equation © Mr. Sims What is the average speed of a runner who completes a 10,000 meter race in 25 minutes? D = rt 10,000 = r(25) r = 400 m/min © Mr. Sims You are going on a trip with some friends and you have $85 to help pay for gas. It costs $22 to fill the tank. How many times can you completely fill the tank? How much money will you have left? If this problem is represented by the equation 22x + y = 85, what do the 22, the x, the y, and the 85 represent? 22 x y 85 dollar cost of a tank of gas number of times you can fill the tank dollar amount left dollar amount available © Mr. Sims Algebra 1 Section 1.5 Assignment Check whether the given number is a solution of the equation. 1.) 3 + 2x = 9, 2 3.) 6x – 4 = 3, 1 2.) 2y + y = 2y + 5, 5 Solve the equation. 4.) x + 6 = 11 5.) x – 5 = 1 6.) 2x = 6 7.) x 5 4 8.) 2x – 1 = 9 9.) x3 = 1 Check whether the given number is a solution of the inequality. 10.) 5 + x > 8, 4 11.) 3x – 1 ≥ 7, 3 12.) x – 7 ≥ 11 – x, 9 © Mr. Sims Any rebroadcast, reproduction, or other use of the pictures and materials from this site and presentations, without the express written consent of Mr. Sims, is prohibited. © Mr. Sims. All rights reserved. © Mr. Sims