How can I solve this inequality

-6x+6 < -4x+5 I believe it equals x > 0.5if the answer I was given is correct. Please show the work.also how would I solve |5x-6|+4 ≥ 7

Also how would I find the slope of a line that passes through the points (5,2) , (-2,1)
could you also give a formula that is shown through y intercept form

OK, -6x+6 < -4x+5.
1. subtract 6 from both sides. -6x < -4x -1
2. Add 4x to both sides -2x < -1
3. Divide both sides by -2 and reverse the sign to give x>0.5.

|5x-6|+4 >= 7 has two solutions.
1. subtract 4 from goth sides to give |5x-6| >=3
2. Set up the first equation that 5x-6 >= 3 add 6 to both sides and then divide by 5 to get
x>=9/5 as one solution.
3. The other solution would be found by 5x-6 <=-3 Again, add 6 to both sides and divide by 5 to get
x<= 3/5.

Last one--you're not asking too much are you. m = (y2-y1)/(x2-x1) = (1-2)/(-2-5) = -1/-7 = 1/7

Now y = x/7 + b substitute in one of the ordered pairs for x and y and solve for b. U can do it.

-6x+6<-4x+5, so 1<2x, so x>.5. Forgive me- I don't know how to do the greater than or equal to sign, but the answer is the same.
l5x-6l>3, so 5x-6>3 or 5x-6<-3
x>9/5 or x<3/5
Slope is rise over run, so (2-1)/5--2=1/7
Now use point slope formula with either of the points. Let's go with the first set of points. y-2=1/7(x-5)
In y-intercept form, y=x/7-5/7+14/7
so y=x/7+9/7

1. -6x<-4x+5 First, add 4x to each side
-2x<5 Now, Divide each side by -2 (remember to switch the inequality sign when mult. or div. by negatives)
x>-2.5

2. |5x-6|+4 ≥ 7 Split these up into 2 equations, one with positive value of 5x-6, and 1 with negative value.
Equation 1: 5x-6+4≥7 Simplify
5x-2≥7 Add 2 to each side
5x≥9 Divide each side by 5
x≥1.8
Equation 2: -(5x-6)+4≥7 Simplify
-5x+10≥7 Subtract 10 from each side