Math Problem Statement
Solve the equation to find x. 5(2x + 3) - 7x = 21
Solution
The equation given is:
Let's solve it step by step:
Step 1: Expand the expression
Distribute the across the terms inside the parentheses:
So the equation becomes:
Step 2: Combine like terms
Now, combine the -terms:
This simplifies to:
Step 3: Isolate the variable
Subtract 15 from both sides:
Step 4: Solve for
Finally, divide both sides by 3:
Thus, the solution is:
Let me know if you need further clarification or details on any of the steps.
Here are some related questions to explore further:
- What would happen if the equation had a different constant term on the right-hand side?
- How would you solve the equation if there were fractions involved instead of integers?
- Can you solve for if there was no solution (e.g., parallel lines in a system of equations)?
- What if the equation was quadratic (e.g., had terms)? How would that change the solution process?
- 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