Math CentralQuandaries & Queries

Question from Milan:

how many solutions does 3 (x + 4) = 3 x + 4 have?

Hi Milan,

I can suggest two ways to approach this problem, one geometric and the other algebraic.


The expressions $y = 3(x+4)$ and $y = 3x + 4$ can both be plotted as graphs in the plane and any $x$ value that satisfies $3(x + 4) = 3x+4$ will be the first coordinate of a point where the graphs intersect. Use a table of values for each of $y = 3(x+4)$ and $y = 3x + 4$ to sketch the two graphs and look for points of intersection.


Expand the left side of $3(x + 4) = 3x+4$ using the distributive law. Simplify. What do you see?

Write back if you need more assistance,

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