What is the solution to the inequality below?
12x > 6(x - 2)
To solve the inequality 12x > 6(x - 2), we'll follow these steps:
Step 1: Distribute the 6 to the terms in the parentheses on the right side of the inequality:
12x > 6x - 12
Step 2: Combine like terms on both sides of the inequality:
12x - 6x > -12
6x > -12
Step 3: Divide both sides of the inequality by 6 to isolate the variable x:
(6x)/6 > (-12)/6
x > -2
So, the solution to the inequality 12x > 6(x - 2) is x > -2.
To solve the inequality, we need to find the value(s) of x that make the inequality true. Here's how to do it step by step:
1. Distribute the 6 on the right side of the inequality:
12x > 6x - 12
2. Simplify by combining like terms:
12x - 6x > -12
3. Combine the x terms on the left side:
6x > -12
4. To isolate x, divide both sides of the inequality by 6. Since we are dividing by a positive number, the inequality sign remains the same:
(6x)/6 > (-12)/6
x > -2
Therefore, the solution to the inequality 12x > 6(x - 2) is x > -2.
12 x > 6 x -12 subtract 6 x both sides
6 x > -12 divide both sides by 6
x > -2