did i do this right?

Question

1. solve for x collect x's on left side .. the solution should be presented with x first, then correct inequality symbol, then the number .

2 (x+1)>(s/b greater or equal to sign) 12

2x+2>(greater to and equal sign) 12
2x+2-2(greater to and equal sign) 12+2
2x>(or equal sign) 14


another one solve for x
4x+3-13x-7<(3-4x)


how do i find the slopes?

find the slope of the line that passes through the points
(3,-5) and (-5,-6)



i have no clue what they want here

translate to an algebraic statement, do not solve
three times the sum of a number and seven yields the same result as the twice the same number decreased by four ???????

Answer 1

Must do the exact same thing to both sides of the equation or inequality. In your line 3, you subtracted 2 from the left, but added 2 to the right.
x>=5

4x+3-13x-7<3-4x
-9x - 4 < 3-4x
-5x - 4 < 3
-5x < 7
x > -7/5 (must flip the inequality sign when dividing or multiplying by a negative.)

use the slope formula: (y2-y1)/x2-x1)
(-5 - -6)/(3- -5)
1/8

let x="a number"
sum of a number and seven => x+7
three times that sum => 3(x+7)
yields means "=" in this case
twice the same number => 2x
decreased by four => 2x - 4
altogether:
3(x+7) = 2x -4

Answer 2

1)
2(x+1) >/= 12
2x + 2 >/= 12
2x + 2 - 2 >/= = 12 - 2
2x >/= 10
x >/= 10/2
x >/= 5

2)
4x + 3 -13x -7 < (3-4x)
-9x - 4 < 3 - 4x
-9x - 4 + 4 < 3 - 4x + 4
-9x < 7 - 4x
-9x + 4x < 7 - 4x + 4 x
-5x < 7
x < -7/5

3)
Slope = y2 - y1 / x2 - x1
Point (3, -5) ==> (x1, y1)
Point (-5, -6) ==> (x2, y2)

Slope = -6 - (-5)/ -5 - 3
Slope = -6 + 5 / -8
Slope = - 1/-8
Slope = 1/8

4) Algebraic statement

Three Times = 3
Let x = a number
Sum = +
Seven = 7
Three times the sum of a number and seven =

3( x + 7)
Yields means =
Twice = 2
the same number = x
decrease means " - "
four = 4
Twice the same number decreased by four =

2x - 4

The statement ==> 3(x + 7) = 2x - 4

Answer 3

you messed. you were supposed to subtract 2 from both sides. to get 2x>=10 wich is x>=5
on the other one.you get -9x<=3 then switch the sign because you divide by a negative to get x>=-7/5. for the last one.
you use the formula y2-y1/x2-x1. the slope is 1/8

Answer 4

yes your steps are correct for the first one.

4x + 3 - 13x < 3 - 4x
-9x + 3 < 3 - 4x
-5x < 0
x > 0

slope = (-6 --5)/(-5-3)=-1/-8 = 1/8

let n be the number, then the eq is
3(n+7)=2n-4

Answer 5

yes, the first problem looks right... to find the slope is hard to explain, but you should graph the two points, then find the difference between them on the x and y axis... then you should have your slope!