Math Problem Statement

1+5(x-7)=2-2(x-9)

Solution

Let's solve the equation step-by-step:

1+5(x7)=22(x9)1 + 5(x - 7) = 2 - 2(x - 9)

Step 1: Distribute terms

Expand both sides by distributing the constants into the parentheses:

1+5x35=22x+181 + 5x - 35 = 2 - 2x + 18

Step 2: Simplify each side

Combine like terms on each side:

5x34=2x+205x - 34 = -2x + 20

Step 3: Move variable terms to one side

Add 2x2x to both sides to collect all xx-terms on the left:

7x34=207x - 34 = 20

Step 4: Move constant terms to the other side

Add 3434 to both sides to isolate the xx-term:

7x=547x = 54

Step 5: Solve for xx

Divide by 77 to get:

x=5477.71x = \frac{54}{7} \approx 7.71

So, the solution is:

x=547x = \frac{54}{7}

Would you like further clarification on any of these steps?


Here are some related questions to explore further:

  1. How do you handle equations with multiple distribution steps?
  2. What are common mistakes in distributing terms in equations?
  3. How does isolating variables simplify solving equations?
  4. What methods can be used to verify the solution of an equation?
  5. How can fractions be simplified in the solution process?

Tip: Always double-check your work by plugging the solution back into the original equation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Distributive Property
Solving Equations

Formulas

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

Theorems

Solving linear equations by isolating variables

Suitable Grade Level

Grades 7-8