Math Problem Statement

Solve each equation. Check your solution. 3n + 4 = 7, 9 = 2x + 1, 4c - 6 = 2, -4 = 2t - 2, 3f - 12 = -3, 8 = 4v + 12, 5d - 6 = 9, 2k + 12 = -4, -5 = 3m - 14, 0 = 8z + 8

Solution

Let's go ahead and solve the equations one by one from the image you uploaded.

1. 3n+4=73n + 4 = 7

Subtract 4 from both sides: 3n=743n = 7 - 4 3n=33n = 3 Now, divide by 3: n=1n = 1

2. 9=2x+19 = 2x + 1

Subtract 1 from both sides: 8=2x8 = 2x Now, divide by 2: x=4x = 4

3. 4c6=24c - 6 = 2

Add 6 to both sides: 4c=2+64c = 2 + 6 4c=84c = 8 Now, divide by 4: c=2c = 2

4. 4=2t2-4 = 2t - 2

Add 2 to both sides: 4+2=2t-4 + 2 = 2t 2=2t-2 = 2t Now, divide by 2: t=1t = -1

5. 3f12=33f - 12 = -3

Add 12 to both sides: 3f=3+123f = -3 + 12 3f=93f = 9 Now, divide by 3: f=3f = 3

6. 8=4v+128 = 4v + 12

Subtract 12 from both sides: 812=4v8 - 12 = 4v 4=4v-4 = 4v Now, divide by 4: v=1v = -1

7. 5d6=95d - 6 = 9

Add 6 to both sides: 5d=9+65d = 9 + 6 5d=155d = 15 Now, divide by 5: d=3d = 3

8. 2k+12=42k + 12 = -4

Subtract 12 from both sides: 2k=4122k = -4 - 12 2k=162k = -16 Now, divide by 2: k=8k = -8

9. 5=3m14-5 = 3m - 14

Add 14 to both sides: 5+14=3m-5 + 14 = 3m 9=3m9 = 3m Now, divide by 3: m=3m = 3

10. 0=8z+80 = 8z + 8

Subtract 8 from both sides: 8=8z-8 = 8z Now, divide by 8: z=1z = -1

Let me know if you'd like solutions for the rest of the equations, any clarifications, or further explanations.

Here are 5 related questions to challenge your understanding:

  1. How would the approach differ if a quadratic equation was present?
  2. How would you solve 2x5=3x+12x - 5 = 3x + 1?
  3. How can systems of equations be solved with substitution or elimination?
  4. What method would you use to solve an equation involving fractions?
  5. How would you apply the distributive property to simplify and solve equations?

Tip: Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Basic linear equation solving: ax + b = c

Theorems

Addition property of equality
Multiplication property of equality

Suitable Grade Level

Grades 6-8