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

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Math Problems

Grade 8

Solve multi-step inequalities

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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 $4$ .