Math Problem Statement

Solve the equation to find x. 5(2x + 3) - 7x = 21

Solution

The equation given is:

5(2x+3)7x=215(2x + 3) - 7x = 21

Let's solve it step by step:

Step 1: Expand the expression

Distribute the 55 across the terms inside the parentheses:

5(2x+3)=10x+155(2x + 3) = 10x + 15

So the equation becomes:

10x+157x=2110x + 15 - 7x = 21

Step 2: Combine like terms

Now, combine the xx-terms:

(10x7x)+15=21(10x - 7x) + 15 = 21

This simplifies to:

3x+15=213x + 15 = 21

Step 3: Isolate the variable

Subtract 15 from both sides:

3x=21153x = 21 - 15

3x=63x = 6

Step 4: Solve for xx

Finally, divide both sides by 3:

x=63=2x = \frac{6}{3} = 2

Thus, the solution is:

x=2x = 2

Let me know if you need further clarification or details on any of the steps.


Here are some related questions to explore further:

  1. What would happen if the equation had a different constant term on the right-hand side?
  2. How would you solve the equation if there were fractions involved instead of integers?
  3. Can you solve for xx if there was no solution (e.g., parallel lines in a system of equations)?
  4. What if the equation was quadratic (e.g., had x2x^2 terms)? How would that change the solution process?
  5. How do you verify the solution by substituting back into the original equation?

Tip: Always check your final answer by plugging it back into the original equation to ensure it's correct.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Distributive Property
Combining Like Terms

Theorems

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Suitable Grade Level

Grades 6-8