algebra questions... again?

Question

-6f + 7 < 2f - 9

5/6g - 4 > 2/3g + 6

5.4 -10.9w > 9.1w - 14.6

-2 1/9d + 3/5 < -3 2/9d - 4 2/5

I really, really suck at this stuff. And my teacher is freaking out at me because I don't list the variable first. XD I do these things just to annoy her. XD

Answer 1

I'll show you how to do one or two, and perhaps you can do the rest...

1)
-6f + 7 < 2f - 9

Add 9 to both sides:
-6f + 7 + 9 < 2f
-6f + 16 < 2f

Now add 6f to both sides:
16 < 2f + 6f
16 < 8f

Now divide both sides by 8
2 < f

Reverse it to make your teacher happy:
f > 2

2)
(5/6)g - 4 > (2/3)g + 6

Multiply both sides by the common denominator of 6:
5g - 24 > 4g + 36

Add 24 to both sides:
5g > 4g + 36 + 24
5g > 4g + 60

Subtract 4g from both sides:
g > 60

Things to watch out for...
Adding or subtracting isn't an issue, but If you are ever multiplying or dividing by a negative number you must switch the sign.
For example, if you had:
-5x > 10
Then when you divide by -5, you have to reverse the sign:
x < 10/(-5)
x < -2

Answer 2

-6f +7<2f - 9
7+9 < 2f+6f
16<8f
22

5/6g -4 >2/3g + 6
5/6g -2/3g > 6 + 4
1/6g >10
g>60

5.4 -10.9w > 9.1w -14.6
5.4 +14.6 > 10.9w +9.1w
20 > 20w
1>w or w<1

-2 1/9 d+3/5 < -3 2/9d -4 2/5
-2 1/9 d +3 2/9 d < -4 2/5 -3/5
1 1/9 d < -5
10/9 d<-5
d < -45/10
d< -9/2

Answer 3

-6f-2f<-9-7
-8f<-16
8f>16
f>2

2.(5/6)g-(2/3)g>6+4
multiplying by 6
5g-4g>60
g>60

3.5.4-10.9w>9.1w-14.6
-10.9w-9.1w>-14.6-5.4
-20w>-20
w<1

4.-2 1/9d+3 2/9d<-4 2/5-3/5
-19/9 d+29/9 d<-22/5-3/5
10/9 d<-5
multiplying by 9
10d<-45
d<-4.5

Answer 4

First, locate what x is in y words. which ability to place the x on the left edge of the equation and y and four on the different: x - 2y = 4 Subtract -2y from the two sides: x = 4 - (-2y) Minus minus a minus is a plus: x = 4 + 2y Now locate the y-intercept by utilising placing x = 0: 0 = 4 + 2y or, 4 + 2y = 0 Subtract 4 from the two sides: 2y = -4 Divide the two sides by utilising 2: y = -2, the y-intercept Now, locate what y is in terms of x: x - 2y = 4 Subtract x from the two sides: -2y = 4 - x Divide the two sides by utilising -2: y = (4 - x) / -2 = (4 / -2) - (x / -2) = -2 - (-0.5 x) = -2 + 0.5x y = 0.5x - 2 Now locate the x-intercept by utilising placing y = 0: 0 = 0.5x - 2, or 0.5x - 2 = 0 upload 2 to the two sides: 0.5x = 2 Divide the two sides by utilising 0.5: x = 2 / 0.5 x = 4, the x-intercept Now draw a line on your graph that is going by way of (4, 0) & (0, -2). Slope-intercept type: y = mx + b (to that end b = 0): y = mx, or mx = y Sove for m (the slope): Divide the two sides by utilising x: m = y / x replace from above x = 4, y = -2: m = -2 / 4 m = -0.5 (the slope) The slope is likewise the tangent of the attitude formed by utilising the line and the x-axis.

Answer 5

8f>16
f>2

1/6g>10
g>60

20w<20
w<1

-19/9d +3/5< -29/9d -22/5
10/9d<-5
d<-4.5

Answer 6

-6f+7<2f-9
-6f-2f<-9-7
-8f<-16
8f>16
f>2
Please solve other problems
in a similar way. They are simple.

Answer 7

-8f < -16
f > 2


1/6g > 10
g > 60


-20w > -20
w < 1


1 1/9d < -5
d < -4.5