Solve the inequality. Write the answer in interval notation.
-$| x - 4 | + 7

Name: Solve the inequality. Write the answer in interval notation. -$| x - 4 | + 7 < 10$ A) $\varnothing$ B) (1,7) C) (1,10) D) [1,7]
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Question

Solve the inequality. Write the answer in interval notation.
-$| x - 4 | + 7 < 10$
A)  $\varnothing$
B)  (1,7) 
C)  (1,10) 
D)  [1,7]

Quizplus · Accepted Answer

To solve the inequality $| x - 4 | + 7 < 10$, first subtract 7 from both sides to get $| x - 4 | < 3$. This means $x - 4$ is less than 3 and greater than -3. So, $ -3 < x - 4 < 3 $. Adding 4 to all parts of the inequality gives $1 < x < 7$, which in interval notation is (1, 7).

Solve the Inequality ∣x−4∣+7<10| x - 4 | + 7 < 10∣x−4∣+7<10

Solve the Inequality $| x - 4 | + 7 < 10$