audio read-through Solving More Complicated Linear Equations with Integer Coefficients

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Solving Simple Linear Equations with Integer Coefficients


Solve: $3 - 2x = 5x + 1$
Solution: Write a nice clean list of equivalent equations:
$3 - 2x = 5x + 1$ original equation
$3 = 7x + 1$ add $\,2x\,$ to both sides
$2 = 7x$ subtract $\,1\,$ from both sides
$\frac{2}{7} = x$ divide both sides by $\,7\,$
$x = \frac{2}{7}$ write in the most conventional way


For more advanced students, a graph is available. For example, the equation $\,3 - 2x = 5x + 1\,$ is optionally accompanied by the graph of $\,y = 3 - 2x\,$ (the left side of the equation, dashed green) and the graph of $\,y = 5x + 1\,$ (the right side of the equation, solid purple).

Notice that you are finding the value of $\,x\,$ where these graphs intersect. Click the ‘Show/Hide Graph’ button to toggle the graph.