Now we can use the result to form a solution set in set-builder notation.
{ x | x<0 }
This can be read as all values of x such that x is less than 0.
Extra
Why It Works?
Let's focus on why after distributing -2 we could add 14 to both sides of the inequality, then divide both sides by -6, and the final answer is correct. First, we will recall the Addition Property of Inequality.
Addition Property of Inequality
Adding the same number to both sides of an inequality creates an equivalent inequality. This equivalent inequality will have the same solution as the original inequality.
Because of this, adding 14 to both sides of the inequality does not change the answer. The next property we used is the Division Property of Inequality.
Division Property of Inequality
Dividing both sides of an inequality by the same number creates an equivalent inequality. However, if the number is positive, the inequality sign remains the same. If the number is negative, the inequality sign needs to be reversed to create an equivalent inequality.
Notice that in our solution we divided both sides of the equation by a negative number, -6, and reversed the inequality sign. This means, that the inequality x < 0 has the same answer set as the original inequality -2(3x+7) > -14.
