Question

match the solution type with its corresponding equation.
no solution \t\t a. $2x + 2 = 2x + 2$
one solution \t\t b. $2x + 2 = x + 1$
infinite solutions \t c. $2x + 2 = 2x + 1$

Explanation:

Step1: Analyze Equation a

For equation \(a: 2x + 2 = 2x + 2\), subtract \(2x\) from both sides, we get \(2 = 2\), which is always true. So this equation has infinite solutions.

Step2: Analyze Equation b

For equation \(b: 2x + 2 = x + 1\), subtract \(x\) from both sides: \(x + 2 = 1\), then subtract 2: \(x = - 1\). So this equation has one solution.

Step3: Analyze Equation c

For equation \(c: 2x + 2 = 2x + 1\), subtract \(2x\) from both sides, we get \(2 = 1\), which is false. So this equation has no solution.

Answer:

no solution - c. \(2x + 2 = 2x + 1\)
one solution - b. \(2x + 2 = x + 1\)
infinite solutions - a. \(2x + 2 = 2x + 2\)