Question

not all equations have exactly one solution. consider the equation $2n + 6 = 2(3 + n)$. can you find more solutions? complete the rest of the table. table with n values 0,1,2,3 and solution? column, 0 has solution, 1,2,3 have ?

Explanation:

Step1: Simplify the right-hand side

$2(3 + n) = 6 + 2n$

Step2: Compare both sides of equation

Left-hand side: $2n + 6$; Right-hand side: $2n + 6$

Step3: Test n=1 in the equation

Left: $2(1)+6=8$; Right: $2(3+1)=8$

Step4: Test n=2 in the equation

Left: $2(2)+6=10$; Right: $2(3+2)=10$

Step5: Test n=3 in the equation

Left: $2(3)+6=12$; Right: $2(3+3)=12$

Answer:

n	Solution?
1	solution
2	solution
3	solution

This equation is an identity, so all real numbers are solutions.