Questions: Solve, [ y-20<-13 ] If all real numbers are solutions, click on "All reals". If there is no solution, click on "No solution".

Solve, [ y-20<-13 ] If all real numbers are solutions, click on "All reals". If there is no solution, click on "No solution".
Transcript text: Solve, \[ |y|-20<-13 \] If all real numbers are solutions, click on "All reals". If there is no solution, click on "No solution".
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Solution

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Solution Steps

Step 1: Rewrite the inequality

The given inequality is: \[ |y| - 20 < -13 \] Add 20 to both sides to isolate the absolute value term: \[ |y| < -13 + 20 \] \[ |y| < 7 \]

Step 2: Solve the absolute value inequality

The inequality \( |y| < 7 \) means that \( y \) is between \(-7\) and \(7\). Therefore: \[ -7 < y < 7 \]

Step 3: Interpret the solution

The solution to the inequality is all real numbers \( y \) such that \( y \) is greater than \(-7\) and less than \(7\). This is a valid range of solutions, so the answer is not "All reals" or "No solution."

Final Answer

\(-7 < y < 7\) or \( \boxed{(-7, 7)} \)

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