Math Problem Statement

-2(x + 3) + 1 = -7

Solution

To solve the equation 2(x+3)+1=7-2(x + 3) + 1 = -7 for xx, follow these steps:

  1. Distribute the 2-2 across the parentheses: 2(x+3)=2x6-2(x + 3) = -2x - 6 So the equation becomes: 2x6+1=7-2x - 6 + 1 = -7

  2. Combine like terms on the left side: 2x5=7-2x - 5 = -7

  3. Add 5 to both sides to isolate the term with xx: 2x=7+5-2x = -7 + 5 2x=2-2x = -2

  4. Divide both sides by 2-2 to solve for xx: x=22=1x = \frac{-2}{-2} = 1

So, the solution is x=1x = 1.

Would you like more details, or do you have any questions?

Here are five related questions to further your understanding:

  1. What is the next step if you had 3(x+4)+2=8-3(x + 4) + 2 = -8?
  2. How do you handle equations where the distribution results in both positive and negative terms?
  3. What happens if, after combining like terms, the variable term is zero?
  4. Can you describe how to check if your solution is correct by substituting x=1x = 1 back into the original equation?
  5. How would the process change if the equation involved fractions?

Tip: Always perform the same operation on both sides of an equation to maintain balance.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Distributive Property

Formulas

Distributive property: a(b + c) = ab + ac
Linear equation solving: ax + b = c

Theorems

Distributive Property
Properties of Equality

Suitable Grade Level

Grades 7-9