Graph the solution set to the equality -2 (x + ^) < 4x Show your work or explain
To graph the solution set to the inequality -2(x + ^) < 4x, we need to first simplify the inequality:
-2(x + ^) < 4x
Using the distributive property, we can simplify it further:
-2x - 2(^) < 4x
Now, we need to isolate the variable x by moving all the terms involving x to one side of the inequality:
-2x - 4x < 2(^)
Next, we can combine like terms:
-6x < 2(^)
To solve for x, we divide both sides of the inequality by -6. Remember that dividing by a negative number reverses the inequality sign:
x > (2(^)) / -6
Simplifying further:
x > -(^) / 3
Now, we can graph the solution set on a number line. Since x is greater than -(^) / 3, we will use an open circle to indicate that x is not equal to -(^) / 3, and we shade the region to the right of -(^) / 3:
- - - - - - - - - o - - - - - - - - ->
- - - - - - - - - - - - - - - - - - - -
So, the solution set on the number line is x > -(^) / 3.