Multiply all terms by the least common multiple (LCM) of the denominators (4 and 5), which is 20, to clear the fractions.

Here are the answers to all the questions from the image.

1. a) Solve for x in the linear inequality: $\frac{1}{4}(x+2) < \frac{1}{5}x + 3$

Step 1: Multiply all terms by the least common multiple (LCM) of the denominators (4 and 5), which is 20, to clear the fractions.

$$20 \cdot \frac{1}{4}(x+2) < 20 \cdot \frac{1}{5}x + 20 \cdot 3$$ $$5(x+2) < 4x + 60$$

Step 2: Distribute the 5 on the left side.

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