1Cademy - Translating and Simplifying the sum of $$-8$$ and $$-12$$, increased by $$7$$

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Translating and Simplifying 'the sum of $8$ and $-12$ , increased by $3$ '

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Translating and Simplifying 'the sum of $-8$ and $-12$ , increased by $7$ '

To translate and simplify the English phrase "the sum of $-8$ and $-12$ , increased by $7$ ," first convert the wording into an algebraic expression. The keyword "sum" indicates that the first two numbers should be added together, so they are grouped as $-8$ and $-12$ . The phrase "increased by" indicates that $7$ should be added to the result of that sum. Using brackets to enforce the correct order of operations, the translation is:

$[-8 + (-12)] + 7$

To simplify the expression, perform the addition within the brackets first. Adding two negative integers involves adding their absolute values ( $8 + 12 = 20$ ) and retaining the shared negative sign, resulting in $-20$ . Then, add the remaining term: $-20 + 7$ . Since these numbers have different signs, subtract their absolute values ( $20 - 7 = 13$ ) and apply the sign of the number with the greater absolute value. The simplified answer is $-13$ .

Updated 2026-05-01

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OpenStax Intermediate Algebra

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