Learn Before
Example: Solving Hugh's Part-Time Jobs Application with a Linear Inequality in Two Variables
To solve a real-world application involving combinations of two quantities, you can map the problem to an algebraic inequality.
Consider Hugh, who works at a grocery store paying dollars an hour and babysits for dollars an hour. He wants to earn at least dollars a week. Translate into an inequality: Let be the grocery store hours and be the babysitting hours. The inequality modeling this situation is . Graph the inequality: Convert the inequality to slope-intercept form to find the boundary line: Graph the solid boundary line corresponding to this equation and shade the appropriate half-plane to represent the solution set. Find solutions: Any ordered pair within the shaded region or on the solid boundary line represents a valid combination of hours Hugh can work at each job to earn at least dollars.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
Algebra
Related
Graphing
Graphing
Graphing
Graphing
A small business owner is using a linear inequality to model the maximum number of hours two employees can work without exceeding a weekly budget. To visualize this constraint on a graph, place the following steps in the correct order as they would be performed according to the standard procedure.
A logistics coordinator is using linear inequalities to map out delivery zones based on fuel costs and time constraints. Match each graphing rule with the specific condition that triggers it according to the standard procedure.
A facility manager is graphing a linear inequality to ensure office layouts comply with occupancy codes. While following the standard three-step graphing procedure, the manager identifies that a chosen test point is not a solution to the inequality. To correctly represent the solution set, which region of the graph should the manager shade?
An inventory manager is graphing a linear inequality to model warehouse storage capacity. If the boundary line for the inequality passes directly through the origin , the manager can still use as the test point to determine which side of the line to shade.
Interpreting the Results of a Linear Inequality Graph
An urban planner is using the linear inequality to model the maximum population density of a residential block. When following the standard procedure to graph this constraint, the planner first replaces the inequality symbol with an equals sign to obtain the equation of the ________.
Visualizing Environmental Compliance Constraints
Documenting the Visualization of Resource Constraints
A marketing manager uses a linear inequality to model the possible combinations of social media ads and print ads that can be purchased within a fixed monthly budget. After the manager graphs the boundary line and shades the appropriate region, what do the ordered pairs located within that shaded region represent?
A marketing analyst is graphing a linear inequality to visualize a budget constraint between two advertising channels. To determine which side of the boundary line to shade, the analyst prepares to select a test point according to the standard three-step procedure. What is the mandatory requirement for the point the analyst chooses?
Graphing
Graphing
Graphing
Graphing
Graphing
Graphing
Graphing
Graphing
Example: Solving a Part-Time Job Income Application with a Linear Inequality in Two Variables
Example: Solving Hugh's Part-Time Jobs Application with a Linear Inequality in Two Variables
Example: Solving Veronica's Part-Time Jobs Application with a Linear Inequality in Two Variables
Solving a System of Linear Inequalities by Graphing
Learn After
Hugh works two part-time jobs to save for his college expenses. He earns 10 dollars per hour at a grocery store and 13 dollars per hour babysitting. He wants to earn at least 260 dollars per week. If represents the number of hours he works at the grocery store and represents the number of hours he spends babysitting, which inequality correctly models Hugh's goal?
Hugh works at a grocery store earning dollars per hour and babysits for dollars per hour. He uses the inequality to model his goal of earning at least a week. Match each component of this mathematical model to the real-world value it represents.
Hugh models his goal of earning at least a week from two jobs using the inequality . True or False: In the graph of this inequality, the solid boundary line indicates that combinations of hours earning exactly dollars are included in the solution set.
Hugh is working two jobs—one at a grocery store earning 10 dollars per hour and one babysitting for 13 dollars per hour—to earn at least 260 dollars a week. To find the combinations of hours he can work, he models and graphs the situation using a linear inequality. Arrange the following steps in the correct order to represent this modeling process.
Hugh, an adult learner balancing his studies, earns an hour at a grocery store () and an hour doing freelance administrative work (). To earn at least a week to cover his expenses, he uses the linear inequality . When graphing this inequality to visualize his work options, any ordered pair representing a valid combination of hours will fall either on the solid boundary line or within the ____ region.