QuestionWeek 15 - Inequalities Questi
Solve the inequality. $|5 x+8|+9<2$

Studdy Solution

STEP 1

1. The inequality involves an absolute value expression.
2. We will need to isolate the absolute value term and split the inequality into two separate inequalities to solve it.

STEP 2

1. Isolate the absolute value expression $|5x + 8|$ .
2. Split the absolute value inequality into two separate inequalities.
3. Solve each inequality.
4. Combine the solutions.

STEP 3

First, subtract 9 from both sides of the inequality to isolate the absolute value expression:
$|5x + 8| + 9 < 2$ $|5x + 8| < 2 - 9$ $|5x + 8| < -7$

STEP 4

Recognize that an absolute value expression is always non-negative, meaning $|5x + 8| \geq 0$ . Therefore, it can never be less than a negative number.
Since $|5x + 8| < -7$ is impossible (as absolute values cannot be negative), there are no solutions to this inequality.
The solution to the inequality is:
No solutions exist.

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