\[ 7(2q + 8) + 15q = 105 \] - Imagemakers
Solving 7(2q + 8) + 15q = 105: Step-by-Step Guide
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?
Understanding the Context
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.
Step 1: Expand the Parentheses
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Key Insights
Apply the distributive property to expand 7(2q + 8):
7 × 2q = 14q
7 × 8 = 56
So:
14q + 56 + 15q = 105
Step 2: Combine Like Terms
Combine the q terms:
14q + 15q = 29q
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Now the equation is:
29q + 56 = 105
Step 3: Isolate the Variable Term
Subtract 56 from both sides to isolate the term with q:
29q + 56 - 56 = 105 - 56
29q = 49
Step 4: Solve for q
Divide both sides by 29:
q = 49 ÷ 29
q = 49/29
Final Answer
✅ q = 49/29
or approximately q ≈ 1.69 (when rounded to two decimal places)
