1Cademy - Simplifying $$6 - (-13)$$ and $$-5 - (-1)$$ by Adding the Opposite

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Simplifying $9 - (-15)$ and $-7 - (-4)$ by Adding the Opposite

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Simplifying $6 - (-13)$ and $-5 - (-1)$ by Adding the Opposite

These partnered computations demonstrate that subtracting a negative number is exactly the same as adding the corresponding positive number:

$6 - (-13) = 19$ and $6 + 13 = 19$ : Both expressions equal $19$ , illustrating that $6 - (-13) = 6 + 13$ .
$-5 - (-1) = -4$ and $-5 + 1 = -4$ : Both expressions equal $-4$ , illustrating that $-5 - (-1) = -5 + 1$ .

This demonstrates that the rule $a - (-b) = a + b$ consistently applies to both positive and negative initial values.

Updated 2026-05-01

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OpenStax Intermediate Algebra

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Intermediate Algebra @ OpenStax

Ch.1 Foundations - Intermediate Algebra @ OpenStax

Algebra

A technician is monitoring a cooling system where the temperature deviation is -7 degrees. They need to subtract a negative adjustment of -4 degrees. The calculation is -7 - (-4). According to the rule of adding the opposite, which expression is equivalent to -7 - (-4)?
A project manager is adjusting a resource log. To simplify the calculation of subtracting a negative variance of 15 hours from a scheduled 9 hours, written as 9 - (-15), the manager applies the rule of 'adding the opposite' and rewrites the expression as 9 + ____.
A logistics coordinator is reconciling inventory records. When an 'item return' (modeled as a negative adjustment) is removed from a ledger, the coordinator uses the rule of 'adding the opposite' to simplify the entry. Match each original subtraction record with its equivalent simplified addition expression.
A quality control technician is adjusting a measurement log that has a current baseline of -7. To remove a negative error of -4 from the log, the technician writes the expression -7 - (-4). True or False: According to the rule of 'adding the opposite,' the technician can correctly simplify this expression to -7 + 4.
Simplifying Budget Adjustments
A payroll administrator is correcting an error on an employee's earnings statement. A negative deduction (a refund) of $15 $dollars was incorrectly applied and now must be subtracted from the current $9$ dollar adjustment, written mathematically as $9 - (-15)$. Arrange the following steps in the correct order to simplify this calculation using the 'add the opposite' rule as described in your course materials.
Reconciling Billing Adjustments
The Rule of Adding the Opposite in Ledger Adjustments
Simplifying $6 - (-13)$ and $-5 - (-1)$ by Adding the Opposite
A software developer is documenting the logic for a payroll system that handles employee reimbursements and deductions. To verify the system's accuracy, they use the examples $9 - (-15) = 24 $and$ -7 - (-4) = -3$. Based on these examples, which general mathematical rule is being recalled and confirmed for the subtraction of a negative integer?
A retail store manager is reconciling a cash account that shows a balance of -$7. To remove a negative adjustment of -$4, the manager uses the subtraction -7 - (-4). By applying the rule of 'adding the opposite,' the manager simplifies this to -7 + 4. Based on the paired computations in your training, what is the final result of this calculation?

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