Video: Solving an Equation with One Root by Graphing

The graph in the diagram represents the function 𝑓(𝑥) = 2𝑥 − 7. Without performing any calculation, use the graph to solve 2𝑥 − 7 = 0.

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Video Transcript

The graph in the diagram represents the function 𝑓 of 𝑥 equals two 𝑥 minus seven. Without performing any calculation, use the graph to solve two 𝑥 minus seven equals zero.

The point at which two 𝑥 minus seven equals zero is the point where it crosses the 𝑥-axis, where the 𝑦-coordinate is equal to zero. In this case, we can see that the function two 𝑥 minus seven crosses the 𝑥-axis at 3.5. Therefore, our solution is 𝑥 equals 3.5.

We could check this by solving the equation two 𝑥 minus seven equals zero using the balancing method. Adding seven to both sides of our equation gives us two 𝑥 is equal to seven. And finally, dividing both sides of this equation by two gives us an answer 𝑥 equals seven divided by two, which is equal to 3.5.

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