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Absolute value inequalities can seem tricky at first, but they’re easier to tackle when you break them down step by step. Absolute value represents distance on a number line. That will typically be a positive value, but importantly (especially for this little inside joke of a problem) does not have to be positive.

As is precisely the case in this problem, absolute value can return a non-negative value of zero. In this example, we can first isolate the absolute value. Subtract 4 from both sides to get ∣3x−7∣≤0. Notice something? The absolute value is already non-negative, so for it to equal zero, the expression inside the bars must be exactly zero.

This simplifies to 3x−7=0, leading eventually to x = 7/3. Although we would often split such inequalities into two cases, there's no need to here.

What makes absolute value inequalities interesting is their connection to distance. Problems like this help us think critically about the structure of equations and the constraints they impose. When you approach these with patience and logical steps, you’ll find they’re less intimidating and even a little fun to solve!

#MathMeme #AbsoluteValue #LearnMath

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