Answer:
No and Yes.
Step-by-step explanation:
The inequation is y ≥-x+7 and the pair is (x,y)=(-1,-1). Then:
-1≥ -(-1)+7
-1 ≥ 1+7
-1 ≥ 8, but this is not true, so (-1,-1) is not a solution of y ≥-x+7.
On the other hand, the inequation is y>(3/4)x-5 and the pair is (5,3). Then:
3>(3/4)(5)-5
3>(15/4)-5
3> -5/4 and this is true, so (5,3) is a solution of y>(3/4)x-5.
X=3
Let's solve your equation step-by-step.
−
|
x
−
4
|
+
2
=
−
2
x
+
7
Step 1: Add -2 to both sides.
−
|
x
−
4
|
+
2
+
−
2
=
−
2
x
+
7
+
−
2
−
|
x
−
4
|
=
−
2
x
+
5
Step 2: Divide both sides by -1.
−
|
x
−
4
|
−
1
=
−
2
x
+
5
−
1
|
x
−
4
|
=
2
x
−
5
Step 3: Solve Absolute Value.
|
x
−
4
|
=
2
x
−
5
We know either
x
−
4
=
2
x
−
5
or
x
−
4
=
−
(
2
x
−
5
)
x
−
4
=
2
x
−
5
(Possibility 1)
x
−
4
−
2
x
=
2
x
−
5
−
2
x
(Subtract 2x from both sides)
−
x
−
4
=
−
5
−
x
−
4
+
4
=
−
5
+
4
(Add 4 to both sides)
−
x
=
−
1
−
x
−
1
=
−
1
−
1
(Divide both sides by -1)
x
=
1
x
−
4
=
−
(
2
x
−
5
)
(Possibility 2)
x
−
4
=
−
2
x
+
5
(Simplify both sides of the equation)
x
−
4
+
2
x
=
−
2
x
+
5
+
2
x
(Add 2x to both sides)
3
x
−
4
=
5
3
x
−
4
+
4
=
5
+
4
(Add 4 to both sides)
3
x
=
9
3
x
3
=
9
3
(Divide both sides by 3)
x
=
3
Check answers. (Plug them in to make sure they work.)
x
=
1
(Doesn't work in original equation)
x
=
3
(Works in original equation)
Answer:
Step-by-step explanation:
We have 2 equations represented by the lines on the graph
5x + 4y = 20
2x - 6y = 12
To plot the first equation on the graph, we a assume different points
4y = 20 - 5x
y = (20-5x)/4
y = 5 - 5x/4
If x =0, y = 5
If x = 2, y = 2.5
If x = 4, y = 0,
These points corresponds to the first line that cuts the positive y axis.
The first line that cuts the positive y axis is represented by the equation,
5x + 4y = 20
Since the left region of the line representing equation is shaded, the unshaded side represents
5x + 4y lesser than 20
To plot the second equation on the graph, we a assume different points
-6y = 12-2x
y = (2x-12)/6 = x/3 - 2
if x= 0, y = -2
If x = 3,y = 1
These points corresponds to the second line that cuts the negative y axis.
The second line that cuts the negative y axis is represented by the equation,
2x -6y = 12
Since the downward region of the line representing the equation is shaded, the unshaded side represents
2x -6y greater than 12
Answer:
27. <
28. <
29. =
30. =
Step-by-step explanation:
For absolute value, the value can never be negative unless a negative sign is in front of the absolute value equation. For example |-4| is positive 4 ,but -|-4| is -4. Another way is if you know what multiplying each sign is.
For the fractions, you need to change the fractions to a equal denominator. Hope this helps.
