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Simplifying Before Solving
To simplify the equation before attempting to solve it, apply the process of simplification to each side separately. On the left side, rearrange the terms using the Commutative Property of Addition to group like terms together: . Then, combine the like terms. The -terms simplify to , and the constant terms simplify to . The result is the simplified equation . Notice that the right side, , is already fully simplified. This process prepares the equation for solving by isolating the variable.
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Solving by Simplifying Both Sides
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Simplifying Before Solving
A logistics coordinator is using the equation 3(u + 10) + 4u = 170 to calculate the cost per unit 'u' for a shipment. What is the recommended first step to simplify the left side of this equation?
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A logistics manager is simplifying a formula to determine total shipping costs. To prepare each side of the equation independently before isolating the variable, the manager should combine like terms and apply the __________ property.
A warehouse coordinator is working with an inventory equation. True or False: When simplifying an expression on one side of the equals sign—for example, by combining like terms—the coordinator must perform the exact same operation on the other side of the equation at the same time.
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A data analyst is simplifying a revenue formula before solving for a missing variable. According to standard algebraic procedures for multi-step equations, which two techniques are primarily used to simplify the expressions on either side of the equation independently?
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Solving Using the Addition Property
An office manager is reconciling a supply order using the equation 9x - 5 - 8x - 6 = 7, where x represents the cost of a single unit. According to the standard procedure for simplifying equations by combining like terms, what is the simplified form of the left side of this equation?
A logistics coordinator is reconciling a shipment manifest using the equation 9x - 5 - 8x - 6 = 7, where x represents the value of one box. Match each part of the equation or simplification step with its correct description or result based on the standard procedure for combining like terms.
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A logistics coordinator is simplifying the shipment equation $9x - 5 - 8x - 6 = 7$ to determine the unit cost of missing items. Arrange the following steps for simplifying the left side of this equation in the correct chronological order as described in the standard procedure for combining like terms.
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A labor analyst is simplifying the payroll equation $9x - 5 - 8x - 6 = 7$ to determine a budget variance. After combining the like terms on the left side of the equation, the analyst finds that the simplified equation is ____ = 7.
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A warehouse supervisor is simplifying an inventory reconciliation equation: $9x - 5 - 8x - 6 = 7. To make the equation easier to solve, the supervisor rearranges the terms on the left side to group the variable terms and constant terms together, resulting in: $9x - 8x - 5 - 6 = 7. Which mathematical property is used to justify this rearrangement of terms?
A project coordinator is simplifying the budget variance equation $9x - 5 - 8x - 6 = 7-5-6$, what is the resulting value as described in the standard procedure?