Math Problem Statement

Solving One-Step Equations WS 24 - 25 (1).pdf

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Solution

The document you've uploaded contains a set of one-step equations, followed by some word problems and expressions for simplification. Below, I'll solve the equations in sequence for clarity:

One-Step Equations:

  1. x + 12 = 7

    • Solution: x=712=5x = 7 - 12 = -5
  2. 4 = -0.8n

    • Solution: n=40.8=5n = \frac{4}{-0.8} = -5
  3. 6 = -w/8

    • Solution: w=6×(8)=48w = 6 \times (-8) = -48
  4. 5/6 = 1/3 + d

    • Solution: d=5613=5626=36=12d = \frac{5}{6} - \frac{1}{3} = \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}
  5. x - 8π = π

    • Solution: x=π+8π=9πx = π + 8π = 9π
  6. -4/5 = -5/6k

    • Solution: k=4/55/6=2425k = \frac{-4/5}{-5/6} = \frac{24}{25}
  7. 7x = 35

    • Solution: x=35/7=5x = 35 / 7 = 5
  8. -2 = 6/7n

    • Solution: n=2×76=146=73n = \frac{-2 \times 7}{6} = -\frac{14}{6} = -\frac{7}{3}
  9. 72 = -m

    • Solution: m=72m = -72
  10. r/π = 7.3

    • Solution: r=7.3πr = 7.3π
  11. d - 2.8 ÷ 0.2 = -14

    • Solution: d14=14    d=14+14=0d - 14 = -14 \implies d = -14 + 14 = 0
  12. m - (1/4) · 3 = -5/6

    • Solution: m3/4=5/6    m=5/6+3/4=10+912=1/12m - 3/4 = -5/6 \implies m = -5/6 + 3/4 = \frac{-10 + 9}{12} = -1/12

Word Problems:

  1. Concert Ticket Problem:

    • Equation: p14.50=53p - 14.50 = 53
    • Solution: p=53+14.50=67.50p = 53 + 14.50 = 67.50 (Original price of the ticket is $67.50)
  2. Account Balance Problem:

    • Equation: 420=76×Original balance420 = \frac{7}{6} \times \text{Original balance}
    • Solution: Original balance=420×67=360\text{Original balance} = \frac{420 \times 6}{7} = 360
    • Interest earned: 420360=60420 - 360 = 60

Simplify the Expressions:

  1. 4x + 9 - 6x - y

    • Simplified: 2x+9y-2x + 9 - y
  2. 10 - 5(9n - 9)

    • Simplified: 1045n+45=5545n10 - 45n + 45 = 55 - 45n
  3. -5n + 3(6 + 7n)

    • Simplified: 5n+18+21n=16n+18-5n + 18 + 21n = 16n + 18

Extra Credit:

  1. 12πx = 12π
    • Solution: x=1x = 1

Would you like further details on any particular question? Here are 5 related problems you might find interesting:

  1. Solve: 3x+5=173x + 5 = 17
  2. Simplify: 7(2x+3)4x7(2x + 3) - 4x
  3. What is the original balance if 4/5 of it equals 320?
  4. A discounted price is $25 less than the original price of $75. What's the original price?
  5. If a+b=ca + b = c, and a=5a = 5, c=12c = 12, what is bb?

Tip: Always double-check your solution by substituting the variable back into the original equation to verify its correctness.

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Math Problem Analysis

Mathematical Concepts

Algebra
Equations
Simplification

Formulas

x + a = b
ax = b
Simplification of expressions

Theorems

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Suitable Grade Level

Grades 6-8