Equations with one, no, or infinitely many solutions

Front

What is an equation with no solution?

Back

An equation with no solution is one where no value of the variable can satisfy the equation. For example, the equation 5 = 3 has no solution.

Front

What does it mean if an equation has infinitely many solutions?

Back

An equation has infinitely many solutions if any value of the variable satisfies the equation. For example, the equation 2x = 2(x) has infinitely many solutions.

Front

Solve: 5.5 - x = -4.5 - x

Back

No Solution

Front

Find the solution to the equation: -13 + 5a = 3(a - 3)

Back

a = 2

Front

What is the solution to the equation: 3x + 15 = 3(x + 5)?

Back

Infinitely Many Solutions

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = 0.

Front

What is the first step in solving an equation?

Back

The first step in solving an equation is to isolate the variable on one side of the equation.

Front

What does it mean to isolate a variable?

Back

To isolate a variable means to manipulate the equation so that the variable is alone on one side, making it easier to solve.

Front

Solve: 1/3(2b + 9) = 2/3(b + 9/2)

Back

Infinitely Many Solutions

Front

What is the difference between one solution and no solution?

Back

One solution means there is exactly one value that satisfies the equation, while no solution means there is no value that satisfies the equation.