Equations: One, No, Infinite Solutions

One Solution

• An equation with one solution has a unique value for the variable that satisfies it.
• Example: The equation 5 − 2𝑥 = 2𝑥 − 5 results in one solution.

No Solution

• An equation with no solution has no values of the variable that can satisfy it, indicating a contradiction.
• Example: The equation 9(3𝑥 − 5) = 9(3𝑥 + 5) results in no solution.

Infinite Solutions

• An equation that results in infinite solutions means that the equation is true for all values of the variable.
• Example: The equation 6(2𝑥 + 4) = 3(4𝑥 + 8) yields infinite solutions.

Infinite Solutions Specific Case

• The equation 6𝑥 − 7 = −7 + 6x demonstrates infinite solutions since it simplifies to an identity.

No Solution Specific Case

• The equation 3𝑥 + 4 = −4 + 3x is an example that leads to no solution, presenting a contradiction.

One Solution Specific Case

• The equation 9𝑥 + 4 = 7𝑥 + 4 results in one solution, indicating a specific value for x.

Solving for x

• x = 0 can be derived from the equation 2𝑥 + 7 = 7 + x.
• x = 2 is the solution for the equation 6 − 3𝑥 = 3𝑥 − 6.
• For the equation 3(2𝑥 + 1) = 2(2𝑥 + 1), the solution is x = -1/2.
• The equation 6𝑥 − 8 = 8 − 6x results in x = 4/3.
• The solution for 6𝑥 − 12 = 8 − 3x is x = 20/9.
• The equation 3(𝑥 − 1) = 2(2x − 1) + 2 gives the solution x = -3.