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\[x+\frac78=4\\x=4-\frac78\\x=3+1-\frac78\\x=3+\frac88-\frac78\\x=3+\frac{8-7}8\\x=3+\frac18\\x=3\tfrac18\]
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and you can check your result like this: Equation was \[x+\frac78=4\] our solution was \(x=3\tfrac18\). Plugging the solution back into the equation... \[3\tfrac18+\frac78=4\] if this equation holds true, then our solution solves the equation.
\[3+\frac18+\frac78=4\\ 3+\frac{1+7}8=4\\ 3+\frac88=4\\ 3+1=4\\ 4=4\] which is always true.
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