is this correct
solve and graph the solution set
3(x-4) > 7x-9
my steps
3x-12 > 7x-9
3x-7x > -9+12
-4x > 3
(-4x)/(-4) > (3)/(-4)
x< -(3)/(4)
how do i graph it also
well, everything to the left of -.75 is x.
so then am i correct or completely wrong...
Which of the following is the correct graph for x=3 and x=-2?
Your steps to solve the inequality are mostly correct. Here's a detailed explanation with the correct solution:
1. Start with the inequality: 3(x - 4) > 7x - 9.
2. Distribute the 3 on the left side of the inequality: 3x - 12 > 7x - 9.
3. Combine like terms by subtracting 3x from both sides: -12 > 4x - 9.
4. Move the constant term (-9) to the left side by adding 9 to both sides: -3 > 4x.
5. Divide both sides by 4 to isolate x: (-3)/4 > x.
6. Simplify the inequality: x < -3/4.
Now, let's move on to graphing the solution on a number line:
To graph the solution x < -3/4, follow these steps:
1. Draw a number line.
2. Mark a point on the line to represent -3/4.
3. Since x is less than -3/4, shade in the portion of the number line to the left of -3/4.
Your graph should show an open circle at -3/4 and shading to the left side.
Remember that the solution set includes all values less than -3/4, but does not include -3/4 itself (shown as an open circle).