If x⁄2 + 3⁄4 = 5⁄4, what is the value of x?

Simplifying, we have:

x/2 = 2/4

4x = 4

x = 1

Answer: D

A very simple questions on a simple linear equation. Although the simplest way to solve this equation is to just shift ¾ to the RHS and simplify, an alternative approach could be to backsolve.

It’s questions like these where you have to try and apply strategies like backsolving, because, these questions are so simple that you can end up solving the equation, IF backsolving does not work (very often it WILL work). This will help you build confidence in the strategy and that’s what you need if you wish to really utilize such strategies on test day.

Starting with option C, if I plug in 0 in place of x, the equation becomes 0 + ¾ = \(\frac{5}{4}\), which is incorrect. The LHS is actually smaller than the RHS. Option C can be eliminated.

Plugging in 0 made the LHS smaller than the RHS. Plugging in negative values will make the LHS much smaller, hence, options A and B can be eliminated.

When we plug in 1 from option D, ½ + ¾ = \(\frac{5}{4}\), which is true – think about it, 0.5 + 0.75 = 1.25 indeed.
The correct answer option is D.

Hope that helps!

You can go all crazy or realize this:

x/2 + 0.75 = 1.25

x/2=0.5

x has to be 1.

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