Flashcards: Linear Equations in One Variable — 16 cards

What distinguishes a numerical equation from an algebraic equation?

A numerical equation contains known numbers, an algebraic equation uses variables.

How can the numerical equation 7 + 7 = 12 be expressed using a variable?

By replacing an unknown number with a letter.

What is an algebraic equation?

An equality containing one or more variables.

How do you identify the variable in an equation?

Locate the letter or letters whose values are unknown.

What defines a linear equation regarding variable powers?

The maximum power of any variable is 1.

Why is 5x² + 4y = 0 not a linear equation?

Because the power of x is 2, which is greater than 1.

Why is 3x + 4y = 8z – 2x considered linear?

All variables have a maximum power of 1.

Can a linear equation have variables on both sides of the equality sign?

Yes, variables may occur on either or both sides of the equality sign.

Can a linear equation contain more than one variable?

Yes, it may contain more than one variable.

Which equations are examples of linear equations?

5p + 7 = 22, y/2 − 1 = 5, (3/4)q = 9, and 3x + y = 5.

How can an equation be converted into a statement?

By expressing the equality in words.

What does the equation-to-statement activity ask learners to do?

Express given equations as verbal statements.

What must be done to both sides when solving an equation by balancing?

Both sides must be balanced.

What happens to constants when solving an equation using the balancing method?

Constants are terminated or eliminated.

How is the solution of a linear equation in one variable obtained?

By applying balancing operations to eliminate constants while preserving equality.

What must any operation to eliminate a constant in an equation preserve?

It must keep the two sides balanced.