Solving One-Step Equations & Inequalities

Solving One-Step Equations & Inequalities 6th Grade Mathematics Miss Muhr Click to continue

Try to solve without using a calculator!!! 4 Solving Equations: x and ÷ Click on the topics in order to learn moreabout them: 5 Multiplication Property 6 1 Division Property Solving Equations: + and - 7 Inequalities 2 Addition Property 8 Solving an Inequality 3 Subtraction Property Review

Solve Equations using Addition and Subtraction • In an equation, the variable represents the number that satisfies the equation. To solve an equation means to find the value of the variable that makes the equation true. • The process of solving an equation starts with getting the variable on one side of the equation by itself. Each step results in an equivalent equation. Equivalent equations have equal solutions. Return to Main Menu

Addition Property of Equality • If an equation is true and the same number is added to each side of the equation, the produced equivalent equation is also true. • For any real numbers a, b, and c, if a = b, then a + c = b + c. 14 = 1414 + 3 = 14 + 317 = 17 -3 = -3+9 +96 = 6 Click to continue

Solve by Adding Horizontal Method Vertical Method x – 45 = 78+ 45 +45x = 123 x – 45 = 78x – 45 + 45 = 78 + 45x = 123 Check: x – 45 = 78123 – 45 = ? = 7878 = 78 ✓ Add 45 to both sides to get x by itself Return to Main Menu

Subtraction Property of Equality • If an equation is true and the same number is subtracted from each side of the equation, the produced equivalent equation is also true. • For any real numbers a, b, and c, if a = b, then a - c = b - c. 87 = 8787 -17 = 87 -1770 = 70 13 = 13-28 -28-15 = -15 Click to continue

Solve by Subtracting Horizontal Method Vertical Method 24 + x = 61- 24 - 24x = 37 24 + x = 6124 – 24 + x = 61 – 24x = 37 Check:24 + x = 6124 + 37 = ? = 6161 = 61 ✓ Subtract 24 from both sides to get x by itself Return to Main Menu

Solve Equations using Multiplication and Division In an equation x/2 = 6, the variable x is divided by 2. To solve for x, undo the division by multiplying each side by 2. This is an example of the Multiplication Property of Equality. Return to Main Menu

Multiplication Property of Equality • If an equation is true and each side is multiplied by the same nonzero number, the produced equivalent equation is also true. • For any real numbers a, b, and c, if a = b, then ac = bc. • Example: If x = 5, then 3x = 15. Click to continue

Solve by Multiplying (3/5)x = 1/3(5/3) (3/5)x = (1/3) (5/3)x = 5/9 Check:(3/5)x = 1/3(3/5) (5/9) = ? = 1/31/3 = 1/3 ✓ Multiply both sides by the reciprocal to get x by itself Return to Main Menu

Division Property of Equality • If an equation is true and each side is divided by the same nonzero number, the produced equivalent equation is also true. • For any real numbers a, b, and c, c ≠ 0, if a = b, then a/c = b/c. • Example: If x = -20, then x/5 = -20/5 or -4. Click to continue

Solve by Dividing 70 = -5x-5 -5-14 = x Check:70 = -5x70 = ? = -5(-14)70 = 70 ✓ Divide both sides by -5 to get x by itself Return to Main Menu

< > Inequalities • An inequality, similar to an equation, has two expressions split by a symbol that indicates how one expression is related to the other. • In an equation such as 8x = 64, the = sign indicates that the expressions are equivalent. In an inequality, such as 8x > 64, the > sign indicates that the left side is larger than the right side. Return to Main Menu

< > Solving an Inequality ( > “greater than” ) To solve the inequality 8x > 64, follow the same rules that you did for equations. In this example, divide both sides by 8so that x > 8. 8x > 648 8x > 8 This means that x is a value and it is always larger than 8, and never equal to or less than 8. Click to continue

< > Solving an Inequality(< “less than”) 4x < 884 4x < 22 So… xis a value and it is always smaller than 22, and never equal to or greater than 22. Divide both sides by 4 to get x by itself Return to Main Menu

Review:Solving Equations Solve for x. 3 + x = 27 (a.) x = 30 (b.) x = 24 (c.) x = 25 Use pencil and paper if you need to!

TRY AGAIN! You are close! Go back and think about what the Subtraction Property of Equality is… Back to question

CORRECT!! Great work! You remembered to subtract the same number from both sides to produce equivalent equations. Click to continue

TRY AGAIN! Go back and make sure you double check your work… Back to question

Review – Solving Inequalities Solve for x. 9x < 63 (a.) x < 7 (b.) x < 567 (c.) x > 7 Use pencil and paper if you need to!

< > CORRECT!! Awesome! You remembered to isolate the variable on one side in order to solve the inequality. Click to continue

< > Try Again! Remember… use the Division Property to get the variable by itself. Back to question

< > Try Again! Go back and check the direction of your sign in the inequality. Back to question

Click the pencils to return to the title slide for the next student: CONGRATULATIONS!!! You have completed this lesson on Solving Equations and Inequalities

Solving One-Step Equations & Inequalities