Question

how many solutions does the following equation have: 2t + 6 = 2(t + 3) one solution infinite solutions no solution

Explanation:

Step1: Simplify the right - hand side

We use the distributive property \(a(b + c)=ab+ac\). For the expression \(2(t + 3)\), we have \(2\times t+2\times3 = 2t+6\). So the equation \(2t + 6=2(t + 3)\) becomes \(2t+6 = 2t+6\).

Step2: Analyze the number of solutions

If we subtract \(2t\) from both sides of the equation \(2t + 6=2t+6\), we get \(6 = 6\). This is a true statement regardless of the value of \(t\). When we end up with a true statement after simplifying an equation, it means that the equation has infinite solutions.

Answer:

Infinite solutions