Practicing with manufacturing tolerances helps reinforce the algebraic procedure for solving absolute value inequalities. In these applications, the formula $|\text{actual} - \text{ideal}| \leq \text{tolerance}$ is consistently used. For instance, if an ideal rod diameter is $80$ mm with an allowed actual variation of $0.009$ mm, we set up the absolute value inequality $|x - 80| \leq 0.009$. Translating this to $-0.009 \leq x - 80 \leq 0.009$ and solving yields an acceptable diameter range tightly positioned between $79.991$ mm and $80.009$ mm. Similarly, if the ideal machine part diameter is $75$ mm and the tolerance is slightly larger at $0.05$ mm, the resulting inequality $|x - 75| \leq 0.05$ is solved to completely identify the valid acceptable range squarely spanning from $74.95$ mm to $75.05$ mm.