How many real solutions does the equation |2x - 5| = 9 have?

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Study for the 7th Grade Math Test. Explore interactive quizzes featuring multiple-choice questions, detailed hints, and explanations to enhance understanding. Boost your math skills and get ready for your exam efficiently!

Multiple Choice

How many real solutions does the equation |2x - 5| = 9 have?

Explanation:
Absolute value represents distance from zero, so when you see |2x - 5| = 9, you’re looking for all expressions whose distance from zero is 9. That means the inside, 2x - 5, could be 9 or could be -9. Solve each case: - 2x - 5 = 9 → 2x = 14 → x = 7 - 2x - 5 = -9 → 2x = -4 → x = -2 There are two real solutions: x = 7 and x = -2.

Absolute value represents distance from zero, so when you see |2x - 5| = 9, you’re looking for all expressions whose distance from zero is 9. That means the inside, 2x - 5, could be 9 or could be -9.

Solve each case:

  • 2x - 5 = 9 → 2x = 14 → x = 7

  • 2x - 5 = -9 → 2x = -4 → x = -2

There are two real solutions: x = 7 and x = -2.

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