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Core Focus on Linear Equations

Lesson 1.5. Core Focus on Linear Equations. Solving Two-Step Equations. Warm-Up. Write an equation for each statement and solve to determine the unknown number. The sum of a number and twenty is eighty-seven. The quotient of a number and four is negative six.

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Core Focus on Linear Equations

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  1. Lesson 1.5 Core Focus onLinear Equations Solving Two-Step Equations

  2. Warm-Up Write an equation for each statement and solve to determine the unknown number. • The sum of a number and twenty is eighty-seven. • The quotient of a number and four is negative six. • A number decreased by three tenths is one and two tenths. x + 20 = 87; x = 67 x – 0.3 = 1.2; x = 1.5

  3. Lesson 1.5 Solving Two-Step Equations Solve two-step equations.

  4. Good to Know!  To isolate the variable in a two-step equation you must perform two inverse operations. Reminder:  The inverse operations must undo the order of operations. That means you start by undoing addition or subtraction. Then use inverse operations to remove any multiplication or division. ORDER OF OPERATIONS 1. Grouping Symbols (Fraction Bar, Absolute Value, Parentheses) 2. Powers 3. Multiplication & Division (from left to right) 4. Addition & Subtraction (from left to right) Evaluating Expressions Solving Equations

  5. Example 1 Solve the equation for x. Check the solution. 8x – 3 = 85 Add 3 to both sides of the equation. Divide both sides of the equation by 8.  Check the answer. 8x – 3 = 85 + 3 + 3 8x = 88 8 8a x = 11 8(11) – 3 = 85 88 – 3 = 85 85 = 85

  6. Extra Example 1 Solve the equation for x. −34 = 6 − 4x x = 10

  7. Example 2 Solve the equation for x. Check the solution. Subtract 5 from both sides of the equation. Multiply both sides of the equation by 9.  Check the solution.

  8. Extra Example 2 Solve the equation for x. x = 30

  9. Example 3 Use an equation mat to illustrate and solve the equation 2x – 4 = 6. Lay out the variable cubes and integer chips to match the equation. Remove the integer chips from the side with the variable by canceling out four negative integer chips with four positive integer chips (add 4 positive chips to each side).

  10. Example 3 Continued… Use an equation mat to illustrate and solve the equation 2x – 4 = 6. Divide the integer chips on the right side of the mat equally between the two cubes. Write the solution. x = 5

  11. Extra Example 3 Use an equation mat to illustrate and solve the equation. 5x + 1 = −4 x = −1

  12. Example 4 Eight more than 3 times a number is 29. Write and solve an equation to find the value of the number. Write the equation: Three times a number Eight more than Is 29 Solve the equation.  Check the solution. 3x 3x + 8 3x + 8 = 29 – 8 – 8 3x = 21 3 3a x = 7a 3(7) + 8 = 29 21 + 8 = 29 29 = 29

  13. Extra Example 4 Ten less than six times a number is eight. Write an equation and solve to find the value of the number. 6x − 10 = 8; x = 3

  14. Communication Prompt Why is it important to show your work and check your solution when solving an equation?

  15. Exit Problems Solve each equation for x. • 4x + 5 = 49 • 5 – 2x = 25 x = 11 x = –36 x = –10

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