Question

2t + 6 = 2(t + 3) 1/2 + x = 1/3 + x 5 - 9 + 3x = -10 + 6 + 3x n = n 3(n + 1) = 3n + 1 v + 2 = v - 2

Explanation:

Step1: Analyze \(2t + 6 = 2(t + 3)\)

Expand the right - hand side: \(2(t + 3)=2t+6\). So \(2t + 6=2t + 6\), which is an identity (true for all \(t\)).

Step2: Analyze \(\frac{1}{2}+x=\frac{1}{3}+x\)

Subtract \(x\) from both sides: \(\frac{1}{2}=\frac{1}{3}\), which is false (no solution).

Step3: Analyze \(5 - 9+3x=-10 + 6+3x\)

Simplify both sides: Left - hand side: \(5 - 9+3x=-4 + 3x\); Right - hand side: \(-10 + 6+3x=-4 + 3x\). So \(-4 + 3x=-4 + 3x\), which is an identity (true for all \(x\)).

Step4: Analyze \(n = n\)

This is an identity (true for all \(n\)).

Step5: Analyze \(3(n + 1)=3n + 1\)

Expand the left - hand side: \(3(n + 1)=3n+3\). Then we have \(3n + 3=3n + 1\). Subtract \(3n\) from both sides: \(3 = 1\), which is false (no solution).

Step6: Analyze \(v + 2=v - 2\)

Subtract \(v\) from both sides: \(2=-2\), which is false (no solution).

Answer:

• Identities (true for all values of the variable): \(2t + 6 = 2(t + 3)\), \(5 - 9+3x=-10 + 6+3x\), \(n = n\)
• Equations with no solution: \(\frac{1}{2}+x=\frac{1}{3}+x\), \(3(n + 1)=3n + 1\), \(v + 2=v - 2\)