MGSE8.EE.7a One, Infinite, No Solution

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when every value of the variable satisfies the equation, meaning the two sides of the equation are equivalent for all values.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there is no value of the variable that can satisfy the equation, meaning the two sides of the equation are never equal.

Front

Solve: 2(3x - 5) = 6x - 10

Back

Infinite Solutions

Front

Solve: 3x + 15 = 3(x + 5)

Back

Infinitely Many Solutions

Front

Simplify and determine the solution type: 3x - 7 = 3(x - 3) + 2

Back

Infinite Solutions

Front

Solve: 2x + 1 = 2x - 1

Back

No Solution

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

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

Back

The slope indicates the steepness of the line and the direction it goes; a positive slope rises, while a negative slope falls.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What is the difference between one solution and infinite solutions?

Back

One solution means there is exactly one value that satisfies the equation, while infinite solutions mean any value satisfies the equation.