Solve the inequality 2(x - 1) > 3x + 4. What is the solution?

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Q: Solve the inequality 2(x - 1) > 3x + 4. What is the solution?

Solution: 2(x - 1) > 3x + 4 => 2x - 2 > 3x + 4 => -x > 6 => x < -6.

Steps: 7

Step 1: Start with the inequality: 2(x - 1) > 3x + 4.
Step 2: Distribute the 2 on the left side: 2 * x - 2 * 1 > 3x + 4, which simplifies to 2x - 2 > 3x + 4.
Step 3: Now, we want to get all the x terms on one side. Subtract 3x from both sides: 2x - 2 - 3x > 4.
Step 4: This simplifies to -x - 2 > 4.
Step 5: Next, add 2 to both sides to isolate the x term: -x > 4 + 2.
Step 6: This simplifies to -x > 6.
Step 7: To solve for x, multiply both sides by -1. Remember, when you multiply or divide by a negative number, you flip the inequality sign: x < -6.