Math Problem Statement

2x +3 + 5x = -18 Two column proof

Solution

To solve the equation 2x+3+5x=182x + 3 + 5x = -18 using a two-column proof, we can format it as follows:

Steps (Statements)Reasons (Justifications)
1. 2x+3+5x=182x + 3 + 5x = -18Given Equation
2. 7x+3=187x + 3 = -18Combine like terms 2x+5x=7x2x + 5x = 7x
3. 7x=1837x = -18 - 3Subtract 3 from both sides
4. 7x=217x = -21Simplify 183=21-18 - 3 = -21
5. x=217x = \frac{-21}{7}Divide both sides by 7
6. x=3x = -3Simplify 217=3\frac{-21}{7} = -3

Solution:

The solution to the equation is x=3x = -3.


Would you like more details or have any questions?

5 Related Questions:

  1. How would you check if x=3x = -3 is correct in the original equation?
  2. What are some other methods to solve this equation?
  3. How do we apply a two-column proof in geometry compared to algebra?
  4. What happens if there were no solution or infinitely many solutions?
  5. How would this change if the equation involved fractions or decimals?

Tip:

When solving algebraic equations, always check your solution by substituting it back into the original equation to verify its accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Basic equation solving: combining like terms, isolating variables

Theorems

Addition property of equality
Division property of equality

Suitable Grade Level

Grades 6-8