No Solution/Infinite Solution/One Solution

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there are no values for the variable that can satisfy the equation, meaning the lines represented by the equations are parallel.

Front

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

Back

An equation has infinitely many solutions when any value for the variable satisfies the equation, meaning the lines represented by the equations overlap completely.

Front

What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value for the variable that satisfies the equation, meaning the lines represented by the equations intersect at a single point.

Front

Solve for x: 4x - 9 = 3.5x - 9

Back

x = 0

Front

Determine the number of solutions: 12(x + 3) = 4(2x + 9) + 4x

Back

Infinite Solutions

Front

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

Back

x = 1.6

Front

How many solutions does the equation have: −16 + 5n = −7(−6 + 8n) + 3?

Back

One solution

Front

Solve the equation: 5 + 2(n + 1) = 2n

Back

The equation has no solution.

Front

What is the first step in solving a linear equation?

Back

The first step is to simplify both sides of the equation, if possible, by combining like terms.

Front

What is the purpose of isolating the variable in an equation?

Back

Isolating the variable helps to find the value of the variable that makes the equation true.