Graph the solution set to the equality -2 (x + 6) < 4x Explain or show your work
To solve the inequality -2(x + 6) < 4x, we need to simplify the expression on both sides and isolate the variable x. Here's the step-by-step solution:
-2(x + 6) < 4x
-2x - 12 < 4x (Distributed -2 to both terms inside the parentheses)
-2x - 4x < 12 (Combined like terms)
-6x < 12 (Combined like terms)
To isolate x, we need to divide both sides of the inequality by -6. However, since we are dividing by a negative number, we need to flip the direction of the inequality.
-6x/-6 > 12/-6
x > -2
So, the solution to the inequality is x > -2.
To graph this solution set on a number line, we represent -2 with an open circle on the number line since the inequality is strictly greater than. Then we shade the region to the right of -2 to represent all the values greater than -2.
Here's the graph:
| |---|---|---|---|---|---|---|
-4 -3 -2 -1 0 1 2 3 4
Since the inequality is x > -2, the graph should include all values to the right of -2, but not -2 itself.