M3 U1Q1

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all the equations true simultaneously.

Front

What symbols indicate a closed dot when graphing inequalities?

Back

The symbols ≤ (less than or equal to) and ≥ (greater than or equal to) indicate a closed dot.

Front

What does the inequality |x + 4| < 5 represent?

Back

The inequality |x + 4| < 5 represents the range of values for x that are within 5 units of -4, which is -9 < x < 1.

Front

How do you solve the equation |2x + 9| = 15?

Back

To solve |2x + 9| = 15, set up two equations: 2x + 9 = 15 and 2x + 9 = -15. The solutions are x = 3 and x = -12.

Front

What is the formula to find the speed of a plane in still air given its speed with and against the wind?

Back

Let p be the speed of the plane in still air and w be the speed of the wind. The equations are: p + w = distance/time (with wind) and p - w = distance/time (against wind).

Front

What is the definition of an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves representing the solutions of the inequality on a number line or coordinate plane, using open or closed dots to indicate whether endpoints are included.

Front

What is the difference between an open dot and a closed dot in graphing?

Back

An open dot indicates that the endpoint is not included in the solution (using < or >), while a closed dot indicates that the endpoint is included (using ≤ or ≥).

Front

How do you interpret the absolute value in an equation?

Back

The absolute value of a number represents its distance from zero on the number line, regardless of direction.

Front

What is the solution set for the inequality |x - 3| > 4?

Back

The solution set for |x - 3| > 4 is x < -1 or x > 7.