Lesson 12: Solutions to Inequalities in One Variable (Alg1.2.19)

[size=200][b][color=#1e84cc][icon]/images/ggb/toolbar/mode_tool.png[/icon][/color][color=#0000ff]Find a Value, Any Value[/color][/b][/size]

[size=150]Write some solutions to the inequality [math]y\le9.2[/math].[br][/size]Be prepared to explain what makes a value a solution to this inequality.[br]

[size=150]Write one solution to the inequality [math]7\left(3-x\right)>14[/math].[br][/size]Be prepared to explain your reasoning.[br][br]

[size=200][b][color=#1e84cc][icon]/images/ggb/toolbar/mode_tool.png[/icon][/color][color=#0000ff]Part-Time Work[/color][/b][/size]

To help pay for his tuition, a college student plans to work in the evenings and on weekends. He has been offered two part-time jobs: working in the guest-services department at a hotel and waiting tables at a popular restaurant.

[list][*]The job at the hotel pays $18 an hour and offers $33 in transportation allowance per month.[/*][*]The job at the restaurant pays $7.50 an hour plus tips. The entire waitstaff typically collects about $50 in tips each hour. Tips are divided equally among the 4 waitstaff members who share a shift.[/*][/list]The equation [math]7.5h+\frac{50}{4}h=18h+33[/math] represents a possible constraint about a situation.[br]Solve the equation and check your solution.[br]

Here is a graph on a number line. Put a scale on the number line so that the point marked with a circle represents the solution to the equation.

Does one job pay better if:

The student works fewer hours than the solution you found earlier? If so, which job?[br]Be prepared to explain or show how you know.[br]

The student works more hours than the solution you found earlier? If so, which job?[br]Be prepared to explain or show how you know.[br]

Here are two inequalities and two graphs that represent the solutions to the inequalities.

Inequality 1: [math]7.50h+\frac{50}{4}h<18h+33[/math][br]Inequality 2: [math]7.50h+\frac{50}{4}h>18h+33[/math]

Match each inequality with a graph that shows its solution. Be prepared to explain or show how you know.

[size=200][b][color=#1e84cc][icon]/images/ggb/toolbar/mode_pen.png[/icon][/color][color=#0000ff]More practice?[/color][/b][/size]

What is the solution to the inequality [math]-\frac{1}{2}x+6<4x-3[/math]? Be prepared to explain how you know.[br]

Graph the solution to the inequality on the number line.

For each statement:

Use a number line to show which values satisfy the inequality. [br]Express the statement symbolically with an inequality.[br][br]1. The elevator can lift up to 1,200 pounds. Let x represent the weight being lifted by the elevator.

2. Over the course of the senator's term, her approval rating was always around 53% ranging 3% above or below that value. Let x represent the senator’s approval rating.

3. There's a minimum of 3 years of experience required. Let x represent the years of experience a candidate has.