Problem 13 · AMC 8 Stretch
Core
Algebra & Patterns
intelligent-guessing-and-testingwork-backward
Solve \(4(7x + 5) = 9x + 1\). Then plug your answer back in to make sure it really works.
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Answer: x = -1
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Hint 1 of 4
First open up the left side: multiply \(4\) through the parentheses.
Still stuck? Show hint 2 →
Hint 2 of 4
Move all the \(x\) terms to one side and all the plain numbers to the other by subtracting the same thing from both sides.
Still stuck? Show hint 3 →
Hint 3 of 4
You should reach \(19x = -19\).
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Approach: Solve the linear equation, then check by substitution
- Open the parentheses: \(4(7x + 5) = 28x + 20\), so the equation is \(28x + 20 = 9x + 1\).
- Gather the \(x\)'s on one side and the numbers on the other: \(28x - 9x = 1 - 20\), so \(19x = -19\) and \(x = -1\).
- Check by substituting \(x = -1\): left side \(4(7(-1) + 5) = 4(-2) = -8\); right side \(9(-1) + 1 = -8\).
- Both sides equal \(-8\), so \(x = -1\) is correct.
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