Let’s solve the equation step by step:
We are given:
12r + 13 + 5r = 13 + 17r
Step 1: Combine like terms on each side.
On the left side:
12r + 5r =
17r
So left side becomes:
17r + 13
Right side is already:
13 + 17r
Now the equation looks like:
17r + 13 = 13 + 17r
Step 2: Rearrange to compare both sides.
Notice that addition is commutative — meaning order doesn’t matter. So:
13 + 17r is the same as 17r + 13.
So we have:
17r + 13 = 17r + 13
This is always true, no matter what value of r you plug in.
Step 3: What does this mean?
If both sides are identical, then
every possible value of r makes the equation true.
That means there are
infinitely many solutions.
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Final Answer:
infinitely many solutions
Parent Tip: Review the logic above to help your child master the concept of solving equations with infinite or no solutions worksheet.
