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$8a - |a - 5| - 10, \text{ if } a < 4$

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Solve multi-step inequalities

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Q.

8a - |a - 5| - 10, \text{ if } a < 4

Identify Negative Expression: Since $a < 4$ , we know that the expression inside the absolute value, $a - 5$ , will be negative because any number less than $4$ minus $5$ will be less than $0$ . Therefore, $|a - 5|$ will be equal to $-(a - 5)$ to make it positive.
Rewrite Without Absolute Value: Now we can rewrite the expression without the absolute value: $8a - (-(a - 5)) - 10$ .
Distribute Negative Sign: Simplify the expression by distributing the negative sign inside the parentheses: $8a + (a - 5) - 10$ .
Combine Like Terms: Combine like terms: $8a + a - 5 - 10$ .
Further Simplification: Further simplification gives us $9a - 15$ .
Final Simplified Expression: Since we cannot simplify any further without a specific value for $a$ , and we are given that $a < 4$ , this is the simplified expression for any $a$ that is less than $4$ .

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