Learn Before
Solving
To solve the equation , apply a systematic strategy: simplify both sides first, then isolate the variable.
- Simplify both sides: Distribute on both sides of the equation: Next, use the Commutative Property of Addition to rearrange terms so that like terms are adjacent, then combine like terms to simplify each side. On the left side, becomes . On the right side, becomes , and becomes . The equation simplifies to:
- Isolate the variable: To undo the subtraction of , apply the Addition Property of Equality by adding to both sides:
- Check the solution: Substitute for in the original equation to verify: Because both sides are equal, the solution is confirmed.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.2 Solving Linear Equations and Inequalities - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
Related
Solving by Simplifying First
Solving
Collecting Variables and Constants on Separate Sides
Classification of Linear Equations
Solving Using the General Strategy
Solving by Distributing
Solving by Distributing and Combining Like Terms
Solving with Nested Grouping Symbols
Solving by Distributing Decimals and Collecting Terms
In a professional setting, such as a logistics manager calculating the number of shipping containers needed to meet a specific budget, you must solve linear equations systematically. Arrange the following steps of the standard four-step strategy for solving a linear equation in the correct order from start to finish.
A payroll specialist is using a standard four-step strategy to solve a linear equation to determine a staff member's total compensation. Match each step of the strategy with the correct action required.
A small business owner is solving a linear equation to determine the number of units they must sell to reach a break-even point. According to the standard four-step strategy for solving linear equations, what is the fourth and final step the owner should take?
Initiating the Equation Solving Strategy
A logistics coordinator is solving a linear equation to determine a warehouse's reorder point for safety stock. According to the systematic four-step strategy for solving linear equations, the step that involves using the Addition or Subtraction Properties of Equality to move terms so that the variable remains alone on one side is called __________ the variable.
A facilities manager is using the systematic four-step strategy to solve a linear equation representing a warehouse's monthly energy consumption. True or False: According to this strategy, the final step is to simplify the final expressions through arithmetic operations to find the precise numerical value of the variable.
Standardizing the Linear Equation Solving Strategy
Logistics Route Optimization Strategy
A production supervisor is using the systematic four-step strategy to solve a linear equation that models the daily output of a manufacturing line. According to this strategy, which of the following best describes the actions the supervisor should take during the first step, 'Simplify both sides'?
A budget analyst is using the systematic four-step strategy to solve a linear equation representing a department's quarterly spending. After the analyst has successfully isolated the variable, what is the primary objective of the next step, 'Simplify the final expressions'?
Solving with Nested Grouping Symbols
Solving with Nested Grouping Symbols
Strategy for Solving Linear Equations with Decimal Coefficients
Solving by Clearing Decimals
Solving by Clearing Decimals
Solving by Clearing Decimals
Solving
Solving Using a General Strategy
Solving Using a General Strategy
Solving Using a General Strategy
Strategy for Solving Equations with Fraction or Decimal Coefficients
Learn After
A logistics coordinator is solving the equation 3(2y - 1) - 5y = 2(y + 1) - 2(y + 3) to calculate shipping routes. According to the standard strategy for solving linear equations, which mathematical property should be used first to simplify the terms 3(2y - 1) and 2(y + 1)?
A warehouse supervisor is using the equation 3(2y - 1) - 5y = 2(y + 1) - 2(y + 3) to determine the optimal number of storage bins (y) required for a new shipment. Arrange the following steps in the correct order to solve this equation according to the standard algebraic strategy.
A logistics manager is reviewing a report that uses the equation to calculate shipping costs. True or False: After correctly applying the Distributive Property and combining like terms on both sides of the equation, the expression simplifies to .
Project Resource Calibration
An inventory manager is solving the equation to determine the quantity of surplus items () in a warehouse. To simplify the equation, the manager must first distribute the constants into the parentheses. Match each term from the original equation with its correctly distributed equivalent as shown in the first step of the solution process.
Inventory Discrepancy Analysis
A logistics coordinator uses the equation to calculate a fleet adjustment factor (). Following the standard algebraic steps to solve for the variable, the coordinator determines that the final value of is ____.
Documenting Algebraic Problem-Solving Procedures
A project coordinator has simplified a resource allocation equation down to the form . To isolate the variable and find the final adjustment value, the coordinator adds to both sides of the equation. Which mathematical property is being recalled and applied in this step?
A production supervisor is solving the equation to determine the number of assembly line hours () required for a specific batch. After performing the initial distribution, the supervisor arrives at the expression on the left side of the equation. According to the standard algebraic strategy, which mathematical property allows the supervisor to rearrange these terms into so that the like terms are adjacent for easier simplification?