What is a linear equation in one variable?

Solving multi-step problems using linear equations in one variable

Flashcard
•
Mathematics
•
8th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
An equation that can be written in the form ax + b = 0, where a and b are constants and x is the variable.
2.
FLASHCARD QUESTION
Front
What does it mean if an equation has no solution?
Back
It means that there are no values for the variable that can satisfy the equation.
3.
FLASHCARD QUESTION
Front
What does it mean if an equation has infinitely many solutions?
Back
It means that any value for the variable will satisfy the equation, often resulting from an identity.
4.
FLASHCARD QUESTION
Front
What is an identity in mathematics?
Back
An equation that is true for all values of the variable, such as x + 2 = x + 2.
5.
FLASHCARD QUESTION
Front
How do you determine the number of solutions for the equation 2x + 1 = 2x - 1?
Back
By simplifying, you find that 1 = -1, which is a contradiction, indicating no solution.
6.
FLASHCARD QUESTION
Front
What is the solution to the equation 5n - 1 = 5n + 4?
Back
There is no solution, as simplifying leads to -1 = 4, which is false.
7.
FLASHCARD QUESTION
Front
What does it mean if two linear equations are parallel?
Back
They have the same slope but different y-intercepts, resulting in no points of intersection (no solution).
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