This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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1. a) Solve for x in the linear inequality:
Step 1: Multiply all terms by the least common multiple (LCM) of the denominators (4 and 5), which is 20, to clear the fractions.
Step 2: Distribute the 5 on the left side.
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(1)/(4)(x+2) < (1)/(5)x + 3 Step 1: Multiply all terms by the least common multiple (LCM) of the denominators (4 and 5), which is 20, to clear the fractions.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.