Solve the inequality. Other than , graph the solution set on a number line.
12x - 3 > 3(3x - 9)
12x - 3 > 3(3x - 9)
12x - 3 > 9x - 27
3x > -24
x > -8
-2<3-x<8
To solve the inequality 12x - 3 > 3(3x - 9), we need to simplify the expression and isolate the variable x.
Step 1: Distribute the 3 on the right side
12x - 3 > 9x - 27
Step 2: Move all terms containing x to one side and constant terms to the other side
12x - 9x > -27 + 3
3x > -24
Step 3: Divide both sides of the inequality by 3 (since the coefficient of x is 3)
(3x)/3 > (-24)/3
x > -8
The solution to the inequality is x > -8. To graph this on a number line, we can represent it as an open circle at -8 and shade everything to the right of -8, including positive infinity.
To solve the inequality 12x - 3 > 3(3x - 9), we need to simplify and isolate the variable x. Let's go step by step:
1. Distribute 3 on the right side: 3(3x - 9) = 9x - 27.
The inequality becomes: 12x - 3 > 9x - 27.
2. Next, let's move all terms with x to one side by subtracting 9x from both sides:
12x - 9x - 3 > 9x - 9x - 27.
Simplifying further: 3x - 3 > -27.
3. Now, let's isolate x by adding 3 to both sides:
3x - 3 + 3 > -27 + 3.
Simplifying even further: 3x > -24.
4. Finally, divide both sides by 3 to solve for x:
(3x)/3 > (-24)/3.
This simplifies to: x > -8.
So, the solution to the inequality is x > -8.
Now let's graph the solution set on a number line to represent all the values of x that satisfy the inequality:
Step 1: Draw a number line and mark a point at -8.
Step 2: Since the inequality is x > -8, we need to represent this with an open circle at -8.
Step 3: Shade the region to the right of -8, since the solution set consists of all values greater than -8.
The final result is an open circle at -8 with the region to the right shaded. This represents the solution set x > -8 on the number line.