Solving 7(2q + 8) + 15q = 105: Step-by-Step Guide

Understanding how to solve equations like 7(2q + 8) + 15q = 105 is essential for mastering algebra. Whether you're a student learning basic linear equations or looking to sharpen your problem-solving skills, this step-by-step breakdown will help you confidently solve for q.

What is the Equation?

We start with the equation: 7(2q + 8) + 15q = 105

This equation contains parentheses, variables on both sides, and constants. We’ll simplify and isolate q using fundamental algebraic operations.

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Step 1: Expand the Parentheses

Apply the distributive property to expand 7(2q + 8): 7 × 2q = 14q 7 × 8 = 56

So: 14q + 56 + 15q = 105

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Step 2: Combine Like Terms

Combine the q terms: 14q + 15q = 29q

Now the equation is: 29q + 56 = 105

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Step 3: Isolate the Variable Term

Subtract 56 from both sides to isolate the term with q: 29q + 56 - 56 = 105 - 56 29q = 49

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Step 4: Solve for q

Divide both sides by 29: q = 49 ÷ 29 q = 49/29

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Final Answer

✅ q = 49/29 or approximately q ≈ 1.69 (when rounded to two decimal places)

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Why This Equation Matters

Solving linear equations like 7(2q + 8) + 15q = 105 builds a foundation for more complex math topics, including systems of equations, graphing, and real-world applications such as budgeting and physics problems.

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Pro Tips for Solving Linear Equations

• Always simplify parentheses first using the distributive property.
• Combine like terms to simplify the equation.
• Isolate the variable on one side using addition/subtraction.
• Divide both sides by the coefficient to solve for the variable.
• Double-check your answer by substituting back into the original equation.

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Bonus: Graphical Insight

If you graph y = 7(2x + 8) + 15x and y = 105, the intersection at x = 49/29 confirms the solution visually.

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Conclusion

Solving 7(2q + 8) + 15q = 105 is a straightforward yet powerful exercise in algebra. With practice, these steps become second nature—inviting deeper exploration into mathematical reasoning.

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Start mastering algebra today—in understanding equations like this one lies the key to countless future successes in science, engineering, and beyond!