7H.2.3 Flashcard: Equations with Variables on Both Sides

Front

What does it mean when an equation has 'No Solution'?

Back

An equation has 'No Solution' when the two sides of the equation represent parallel lines that never intersect.

Front

What does it mean when an equation has 'Infinite Solutions'?

Back

An equation has 'Infinite Solutions' when both sides of the equation are identical, meaning any value for the variable will satisfy the equation.

Front

Solve: 9y + 8 = 9y - 8

Back

No Solution

Front

Solve: -10y - 6 = -10y - 6

Back

Infinite Solutions

Front

Solve: 30 + 6t = 11t

Back

t = 6

Front

Solve: 3x - x + 4 = 4(2x + 1)

Back

x = 0

Front

Solve: 5y + 34 = -2(-7y + 1)

Back

y = 4

Front

What is the first step in solving an equation with variables on both sides?

Back

The first step is to isolate the variable by moving all terms involving the variable to one side of the equation.

Front

What is the purpose of combining like terms in an equation?

Back

Combining like terms simplifies the equation, making it easier to solve.

Front

What does it mean to isolate a variable in an equation?

Back

Isolating a variable means to manipulate the equation so that the variable is alone on one side, allowing for easy calculation of its value.