Math Problem Statement

Solve the following equations: 1. 2x = 14 2. 4a + 11 = 39 3. 3n - 5 = -8 4. 5m - 7 = 2m - 1

Solution

I see you've uploaded an image containing a few math problems. Let's go through them one by one to verify the answers:

  1. Problem (d):
    2x=142x = 14
    To solve for xx, divide both sides by 2:
    x=142=7x = \frac{14}{2} = 7 So, x=7x = 7. ✅

  2. Problem (e):
    4a+11=394a + 11 = 39
    First, subtract 11 from both sides:
    4a=3911=284a = 39 - 11 = 28
    Now, divide both sides by 4:
    a=284=7a = \frac{28}{4} = 7 So, a=7a = 7. ✅

  3. Problem (f):
    3n5=83n - 5 = -8
    Add 5 to both sides:
    3n=8+5=33n = -8 + 5 = -3
    Now, divide both sides by 3:
    n=33=1n = \frac{-3}{3} = -1 So, n=1n = -1. ✅

  4. Problem (g):
    5m7=2m15m - 7 = 2m - 1
    First, move all the terms with mm on one side:
    5m2m=1+75m - 2m = -1 + 7
    Simplifying:
    3m=63m = 6
    Now, divide both sides by 3:
    m=63=2m = \frac{6}{3} = 2 So, m=2m = 2. ✅

Everything looks correct! Let me know if you'd like more details on any of the steps or if you have additional questions.

Here are some related questions you can explore:

  1. Solve 2x5=152x - 5 = 15.
  2. Solve 6a+2=326a + 2 = 32.
  3. Solve 4n7=5n+24n - 7 = 5n + 2.
  4. Solve 7p+1=3p97p + 1 = 3p - 9.
  5. Solve 8y4=128y - 4 = 12.

Tip: Always double-check your arithmetic when simplifying equations to avoid small mistakes!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebra

Formulas

Basic equation solving: ax + b = c
Rearranging terms to isolate the variable

Theorems

Properties of equality

Suitable Grade Level

Grades 6-8