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Solving Equations with Variable on Both Sides Mastery Guide

Learn to solve equations with variables on both sides and practical problems. Justify steps and solve multistep linear equations efficiently. Master the method for grouping symbols. Practice with examples and tricky fractions to enhance your skills.

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Solving Equations with Variable on Both Sides Mastery Guide

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  1. Solving Equations with the Variable on Both Sides Objectives: • to solve equations with the variable on both sides. • to solve equations containing grouping symbols. • A.4d Solve multistep linear equations. • A.4f Apply these skills to solve practical problems. • A.4b Justify steps used in solving equations.

  2. To solve these equations, Use the addition or subtraction property to move all variables to one side of the equal sign. Solve the equation using the method learned in Chapter 3 Section 3.

  3. 1) 6x - 3 = 2x + 13 -2x -2x 4x - 3 = 13 +3 +3 4x = 16 4 4 x = 4 Be sure to check your answer! 6(4) - 3 =? 2(4) + 13 24 - 3 =? 8 + 13 21 = 21 Let’s see a few examples:

  4. 2) 3n + 1 = 7n - 5 -3n -3n 1 = 4n - 5 +5 +5 6 = 4n 4 4 Reduce! 3 = n 2 Check: 3(1.5) + 1 =? 7(1.5) - 5 4.5 + 1 =? 10.5 - 5 5.5 = 5.5 Let’s try another!

  5. 3) 5 + 2(y + 4) = 5(y - 3) + 10 Distribute first. 5 + 2y + 8 = 5y - 15 + 10 Next, combine like terms. 2y + 13 = 5y - 5 Now solve. (Subtract 2y.) 13 = 3y - 5 (Add 5.) 18 = 3y (Divide by 3.) 6 = y Check: 5 + 2(6 + 4) =? 5(6 - 3) + 10 5 + 2(10) =? 5(3) + 10 5 + 20 =? 15 + 10 25 = 25 Here’s a tricky one!

  6. Let’s try one with fractions! • Steps: • Multiply each term • by the least common • denominator (8) to • eliminate fractions. • Solve for x. • Add 2x. • Add 6. • Divide by 6. 4) 3 - 2x = 4x - 6 3 = 6x - 6 9 = 6x so x = 3/2

  7. 6(4 + y) - 3 = 4(y - 3) + 2y 24 + 6y - 3 = 4y - 12 + 2y 21 + 6y = 6y - 12 - 6y - 6y 21 = -12 Never true! 21 ≠ -12 NO SOLUTION! 3(a + 1) - 5 = 3a - 2 3a + 3 - 5 = 3a - 2 3a - 2 = 3a - 2 -3a -3a -2 = -2 Always true! We write IDENTITY. Two special cases:

  8. Try a few on your own: • 9x + 7 = 3x - 5 • 8 - 2(y + 1) = -3y + 1 • 8 - 1 z = 1 z - 7 2 4

  9. x = -2 y = -5 z = 20 The answers:

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