Writing Equations and Inequalities

Front

What does the inequality 15 + 6x ≤ 100 represent in a real-world context?

Back

It represents a situation where Lazer Zone charges $15 plus $6 per person, and if Andrea has at most $100 to spend, it determines how many people she can invite to play laser tag.

Front

How do you express 'twice a number plus 9 is less than 30' as an inequality?

Back

The inequality is expressed as 2x + 9 < 30.

Front

What is the first step to solve the equation 350 = 270 + 8h for h?

Back

Subtract 270 from both sides to isolate the term with h: 350 - 270 = 8h.

Front

What is the general form of a linear inequality?

Back

A linear inequality can be expressed in the form ax + b < c, ax + b ≤ c, ax + b > c, or ax + b ≥ c, where a, b, and c are constants.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

How can you graph a linear inequality on a number line?

Back

To graph a linear inequality, first graph the corresponding equation as a line, then use a dashed line for < or > and a solid line for ≤ or ≥. Shade the appropriate side of the line based on the inequality.

Front

What does the term 'solution set' refer to in the context of inequalities?

Back

The solution set is the set of all values that satisfy the inequality.

Front

How do you solve the inequality 2x + 9 < 30?

Back

First, subtract 9 from both sides to get 2x < 21, then divide both sides by 2 to find x < 10.

Front

What is a real-world example of a linear equation?

Back

An example is the equation for total cost: C = mx + b, where C is total cost, m is the cost per item, x is the number of items, and b is a fixed cost.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the rate of change of the dependent variable with respect to the independent variable.