Solve the inequality and show the graph of the solution on number line:
x > -1, Solution set: (-1, ∞)
Explanation
This question involves solving a linear inequality in one variable. Following the method shown in Example 3 and Example 5 from the context, we need to expand the brackets, collect like terms, and solve for x. When dividing by a negative number, the inequality sign reverses, but in this case, we divide by a positive number, so the sign remains the same.
Solution Steps
Step 1: Expand both sides of the inequality. 3(1 - x) < 2(x + 4) 3 - 3x < 2x + 8
Step 2: Transpose terms to collect x terms on one side and constant terms on the other. 3 - 8 < 2x + 3x -5 < 5x
Step 3: Divide both sides by 5 (positive number, so inequality sign remains unchanged). -5/5 < x -1 < x or x > -1
Step 4: Write the solution set. The solution set is (-1, ∞).
Step 5: Graphical representation on number line. Draw a number line. Place an open circle at -1 (since -1 is not included). Draw an arrow to the right of -1 to indicate all numbers greater than -1.