1.2 Solving & Writing Equations and Inequalities

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables and constants.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division).

Front

What does it mean for one quantity to be greater than another in an inequality?

Back

It means that the value of the first quantity exceeds the value of the second quantity.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you graph an inequality on a number line?

Back

To graph an inequality, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate side of the circle.

Front

What is the purpose of writing equations to represent real-world situations?

Back

Writing equations helps to model and solve real-world problems by translating them into mathematical language.

Front

What is the first step in solving the equation 5x - 14 = 8x + 4?

Back

The first step is to get all terms involving x on one side and constant terms on the other side.

Front

What does the solution x = -6 represent in the equation 5x - 14 = 8x + 4?

Back

It represents the value of x that makes the equation true, meaning both sides of the equation are equal.

Front

How do you determine when two quantities are equal using an equation?

Back

Set the two expressions equal to each other and solve for the variable.