Solving 2-Step Equations Grade 7 Pre-Algebra Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Let’s warm up : Simplify:   1) (3x - 5)(7x + 2) 2) (2a2 + 3)(5a - 3) 3) (2a + 3)(7a2 - 5) 4) (x + 5)(3x - 6) Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Let’s start "Linear" equations are mathematical expressions that have an equal sign and linear expressions However, variable(s) in linear equations: Cannot have exponents (or powers) For example, x squared or x 2 Cannot multiply or divide each other For example:  "x" times "y" or xy; "x" divided by "y" or x/y Cannot be found under a root sign or square root sign (sqrt) For example:  √ x or the "square root of x"; sqrt (x) Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. It takes two steps to solve an equation or inequality that has more than one operation: Simplify using the inverse of addition or subtraction. Simplify further by using the inverse of multiplication or division. When you multiply or divide an inequality by a negative number, you must reverse the inequality symbol. Copyright © Ed2Net Learning, Inc.

You can solve the problem with the help of algebra tiles. Solve 2x + 1 = 5 You can solve the problem with the help of algebra tiles. 2x + 1 = 5 Model the equation. Remove 1 tile from each side. 2x + 1 – 1 = 5 – 1 2x = 4 Divide each side into two equal groups. 2x = 4 2 2 Simplify. x = 2 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Now you try! Solve x + 5 = 9 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. To solve a two-step equation, first undo addition or subtraction. Then undo multiplication or division. Solve 3x – 6 = 15. Check your solution. 3x – 6 = 15 3x – 6 + 6 = 15 + 6 3x = 21 3 3 x = 7 Add 6 to each side. Simplify. Divide each side by 3. Simplify. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Check: 3x – 6 = 15 3(7) – 6 = 15 21 – 6 = 15 15 = 15 Replace x with 7. Multiply. Simplify. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Now you try! Solve 15x + 3 = 48. Check your solution. Copyright © Ed2Net Learning, Inc.

Solve x - 19 = 17. 4 Check your solution. x - 19 = 17 4 Add to undo the subtraction. Multiply to undo the division. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Check: x - 19 = 17 4 144 - 19 = 17 36 - 19 = 17 17 = 17 Replace x with 144. Do the division first. The solution is 144. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Now you try! Solve x + 13 = 11 4 Check your solution. Copyright © Ed2Net Learning, Inc.

Let the cost of 1 ticket for a child is = x Five children and one adult went to a concert. Adult tickets were $14. The total price for all the tickets was $59. What was the cost of each child’s ticket? Let the cost of 1 ticket for a child is = x Adult tickets were = $14 Total price for the tickets for five children and one adult = $59, Hence, 5x + 14 = 59 5x + 14 – 14 = 59 – 14 5x = 45 5 5 x = 9 Subtract to undo the addition. Divide to undo the multiplication. Copyright © Ed2Net Learning, Inc.

Negative Coefficients Solve 5 – x = 17. 5 – x = 17 -5 + 5 – x = - 5 + 17 0 – x = 12 –x = 12 -1(–x) = -1(12) x = -12 Add -5 to each side. Simplify. 0 – x = -x Multiply each side by -1. Simplify. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Now you try! Solve – x + 6 = 8. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. BREAK Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Solve each equation: 1) 2x - 8 = -10 2) 2x + 9 = 3 3) 4x - 6 = -18 4) 9x - 15 = 39 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Solve each equation: 5) x - 4 = 11 3 6) x + 2 = 0 3 7) - x = 25 5 8) 10 = 3 + x 2 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 9) I bought three shirts that had equivalent retail values. I used a $15 gift certificate at the time of purchase and paid a total of $81.00. How much did each individual shirt cost? Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. 10) Marty ordered three extremely accurate and scientific water-balloon launchers from a mail order catalog (one for himself and two for his friends). The total price including shipping charges was $50. If the total shipping cost was $5, how much did each launcher cost? Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Let’s review "Linear" equations are mathematical expressions that have an equal sign and linear expressions However, variable(s) in linear equations: Cannot have exponents (or powers) For example, x squared or x 2 Cannot multiply or divide each other For example:  "x" times "y" or xy; "x" divided by "y" or x/y Cannot be found under a root sign or square root sign (sqrt) For example: √x or the "square root of x"; sqrt (x) Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Review It takes two steps to solve an equation or inequality that has more than one operation: Simplify using the inverse of addition or subtraction. Simplify further by using the inverse of multiplication or division. When you multiply or divide an inequality by a negative number, you must reverse the inequality symbol. Copyright © Ed2Net Learning, Inc.

You can solve the problem with the help of algebra tiles. Review Solve 2x + 1 = 5 You can solve the problem with the help of algebra tiles. 2x + 1 = 5 Model the equation. Remove 1 tile from each side. 2x + 1 – 1 = 5 – 1 2x = 4 Divide each side into two equal groups. 2x = 4 2 2 Simplify. x = 2 Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. To solve a two-step equation, first undo addition or subtraction. Then undo multiplication or division. Solve 3x – 6 = 15. Check your solution. 3x – 6 = 15 3x – 6 + 6 = 15 + 6 3x = 21 3 3 x = 7 Add 6 to each side. Simplify. Divide each side by 3. Simplify. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Check: 3x – 6 = 15 3(7) – 6 = 15 21 – 6 = 15 15 = 15 Replace x with 7. Multiply. Simplify. Copyright © Ed2Net Learning, Inc.

Solve x - 19 = 17. 4 Check your solution. x - 19 = 17 4 Add to undo the subtraction. Multiply to undo the division. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Check: x - 19 = 17 4 144 - 19 = 17 36 - 19 = 17 17 = 17 Replace x with 144. Do the division first. The solution is 144. Copyright © Ed2Net Learning, Inc.

Let the cost of 1 ticket for a child is = x Five children and one adult went to a concert. Adult tickets were $14. The total price for all the tickets was $59. What was the cost of each child’s ticket? Let the cost of 1 ticket for a child is = x Adult tickets were = $14 Total price for the tickets for five children and one adult = $59, Hence, 5x + 14 = 59 5x + 14 – 14 = 59 – 14 5x = 45 5 5 x = 9 Subtract to undo the addition. Divide to undo the multiplication. Copyright © Ed2Net Learning, Inc.

Negative Coefficients Solve 5 – x = 17. 5 – x = 17 -5 + 5 – x = - 5 + 17 0 – x = 12 –x = 12 -1(–x) = -1(12) x = -12 Add -5 to each side. Simplify. 0 – x = -x Multiply each side by -1. Simplify. Copyright © Ed2Net Learning, Inc.

Copyright © Ed2Net Learning, Inc. Great Job! Remember to do the practice worksheets!!! Copyright © Ed2Net Learning, Inc.