Simplify the following expression by expanding and collecting like terms.
$-(7x+6)+3(-5x-3)$
Give your answer in the form $ax+b$.
Answer (2)
Distribute the negative sign: − ( 7 x + 6 ) = − 7 x − 6 .
Distribute the 3: 3 ( − 5 x − 3 ) = − 15 x − 9 .
Combine the expressions: ( − 7 x − 6 ) + ( − 15 x − 9 ) .
Combine like terms: − 22 x − 15 . The final answer is − 22 x − 15 .
Explanation
Understanding the Problem We are asked to simplify the expression − ( 7 x + 6 ) + 3 ( − 5 x − 3 ) and express it in the form a x + b . This involves distributing the constants and combining like terms.
Distributing the Negative Sign First, distribute the negative sign in the first term: − ( 7 x + 6 ) = − 7 x − 6.
Distributing the Constant Next, distribute the 3 in the second term: 3 ( − 5 x − 3 ) = − 15 x − 9.
Combining Expressions Now, combine the two resulting expressions: ( − 7 x − 6 ) + ( − 15 x − 9 ) .
Combining Like Terms Combine like terms (x terms and constant terms): ( − 7 x − 15 x ) + ( − 6 − 9 ) = − 22 x − 15.
Final Answer The simplified expression is − 22 x − 15 , which is in the form a x + b , where a = − 22 and b = − 15 .
Examples
In real life, simplifying expressions like this can help in budgeting. For example, if you have a certain amount of money and you're spending a portion of it on multiple items, simplifying the expression can help you determine how much money you have left. Suppose you start with no money, then you have a debt of 7 x + 6 dollars and another debt of 5 x + 3 dollars which is tripled. The expression − ( 7 x + 6 ) + 3 ( − 5 x − 3 ) represents your total financial status. Simplifying it to − 22 x − 15 helps you quickly understand your overall debt.
The simplified expression of the original equation is − 22 x − 15 . This is obtained by distributing and combining like terms. The final answer is in the form a x + b where a = − 22 and b = − 15 .
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