Name Date Period Kuta Software – Infinite Algebra 1 Multi-Step Equations Solve each equation

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Name Date Period Kuta Software – Infinite Algebra 1 Multi-Step Equations Solve each equation. 1) -20=-4x – 6x 2) 6 = 1 – 2n + 5 3) 8x – 2 = -9+7X 4) a +5=-Sa+5 5) 4m – 4 = 4m 6) p-1 =5p+3p-8 7) 5p – 14 = 8p + 4 8) p-4 =-9+ P 9) -8 = -(x + 4) 10) 12-4-6x – 3) 11) 14 =-p-8) 12)-17-4x) – 9 13) -18-6k6(1 + 3) 14) 5n+ 34 = -2(1-7) 15) 2(4x – 3) – 8 = 4 + 2x 16) 3 – 5 = -866 +5n) 17) -(1 + 7x) -61-7 – x) = 36 18) -3(4x + 3) +4(6x + 1) = 43 19) 24a – 22-41-60) 20) -5(1 – 5x) + 5(-8x – 2) = -4x – 8.x

The Correct Answer and Explanation is :

Let’s solve each equation step by step:

  1. Equation: -20 = -4x – 6x
  • Combine like terms: -4x – 6x = -10x
  • The equation becomes: -20 = -10x
  • Divide both sides by -10: x = 2
  1. Equation: 6 = 1 – 2n + 5
  • Combine constants on the right: 1 + 5 = 6
  • The equation becomes: 6 = 6 – 2n
  • Subtract 6 from both sides: 0 = -2n
  • Divide both sides by -2: n = 0
  1. Equation: 8x – 2 = -9 + 7x
  • Subtract 7x from both sides: x – 2 = -9
  • Add 2 to both sides: x = -7
  1. Equation: a + 5 = -5a + 5
  • Subtract 5 from both sides: a = -5a
  • Add 5a to both sides: 6a = 0
  • Divide both sides by 6: a = 0
  1. Equation: 4m – 4 = 4m
  • Subtract 4m from both sides: -4 = 0
  • This is a contradiction; thus, there is no solution.
  1. Equation: p – 1 = 5p + 3p – 8
  • Combine like terms: 5p + 3p = 8p
  • The equation becomes: p – 1 = 8p – 8
  • Subtract p from both sides: -1 = 7p – 8
  • Add 8 to both sides: 7 = 7p
  • Divide both sides by 7: p = 1
  1. Equation: 5p – 14 = 8p + 4
  • Subtract 5p from both sides: -14 = 3p + 4
  • Subtract 4 from both sides: -18 = 3p
  • Divide both sides by 3: p = -6
  1. Equation: p – 4 = -9 + p
  • Subtract p from both sides: -4 = -9
  • This is a contradiction; thus, there is no solution.
  1. Equation: -8 = -(x + 4)
  • Distribute the negative sign: -8 = -x – 4
  • Add 4 to both sides: -4 = -x
  • Multiply both sides by -1: x = 4
  1. Equation: 12 – 4 – 6x = -3
    • Combine constants on the left: 12 – 4 = 8
    • The equation becomes: 8 – 6x = -3
    • Subtract 8 from both sides: -6x = -11
    • Divide both sides by -6: x = 11/6
  2. Equation: 14 = -p – 8
    • Add 8 to both sides: 22 = -p
    • Multiply both sides by -1: p = -22
  3. Equation: -17 – 4x = -9
    • Add 17 to both sides: -4x = 8
    • Divide both sides by -4: x = -2
  4. Equation: -18 – 6k = 6(1 + 3k)
    • Distribute on the right: 6 × 1 + 6 × 3k = 6 + 18k
    • The equation becomes: -18 – 6k = 6 + 18k
    • Add 18 to both sides: -6k = 24 + 18k
    • Subtract 18k from both sides: -24k = 24
    • Divide both sides by -24: k = -1
  5. Equation: 5n + 34 = -2(1 – 7n)
    • Distribute on the right: -2 × 1 + -2 × -7n = -2 + 14n
    • The equation becomes: 5n + 34 = -2 + 14n
    • Subtract 5n from both sides: 34 = -2 + 9n
    • Add 2 to both sides: 36 = 9n
    • Divide both sides by 9: n = 4
  6. Equation: 2(4x – 3) – 8 = 4 + 2x
    • Distribute on the left: 2 × 4x + 2 × -3 = 8x – 6
    • The equation becomes: 8x – 6 – 8 = 4 + 2x
    • Combine constants on the left: -6 – 8 = -14
    • The equation becomes: 8x – 14 = 4 + 2x
    • Subtract 2x from both sides: 6x – 14 = 4
    • Add 14 to both sides: 6x = 18
    • Divide both sides by 6: x = 3

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