Solving Linear Equations and Inequalities

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + by = c, where a, b, and c are constants.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. Examples include x < 5, x ≥ 3.

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) until the variable is alone.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves shading a region of the graph that represents all the solutions to the inequality. The boundary line is dashed if the inequality is strict (< or >) and solid if it is inclusive (≤ or ≥).

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

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of y when x = 0.

Front

How do you find the slope of a line given two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the difference between 'and' and 'or' in inequalities?

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.

Front

How do you check if a solution is correct for a linear equation?

Back

To check if a solution is correct, substitute the value of the variable back into the original equation and see if both sides are equal.

Front

What is a common mistake when solving linear equations?

Back

A common mistake is failing to apply the same operation to both sides of the equation, which can lead to incorrect solutions.