Math Problem Statement

−(3x+8)+6= −(7x−9)

Solution

We will solve the equation step by step:

Given equation:

(3x+8)+6=(7x9)-(3x + 8) + 6 = -(7x - 9)

Step 1: Distribute the negative signs.

Distribute the negative sign on both sides:

3x8+6=7x+9-3x - 8 + 6 = -7x + 9

Step 2: Simplify both sides.

On the left-hand side: 3x8+6=3x2-3x - 8 + 6 = -3x - 2 So, the equation becomes: 3x2=7x+9-3x - 2 = -7x + 9

Step 3: Move all terms involving xx to one side and constants to the other.

Add 7x7x to both sides: 3x+7x2=9-3x + 7x - 2 = 9 4x2=94x - 2 = 9

Now, add 2 to both sides: 4x=114x = 11

Step 4: Solve for xx.

Divide both sides by 4: x=114x = \frac{11}{4}

So, the solution is: x=114or2.75x = \frac{11}{4} \quad \text{or} \quad 2.75

Would you like more details on any step or have any questions?

Here are 5 related questions:

  1. How would you solve if the equation involved fractions?
  2. How does distributing negative signs affect an equation?
  3. What is the next step if we had variables on both sides of a more complex equation?
  4. How do you solve equations that involve powers of xx?
  5. What if the equation had decimals instead of fractions?

Tip: Always combine like terms first before moving terms across the equals sign to simplify equations faster.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Distributive Property

Formulas

Distributive Property: a(b + c) = ab + ac

Theorems

Properties of Equality

Suitable Grade Level

Grades 8-10