1. 3x-5<19
3x-5+5<19+5
3x<24
3x/3<24/3
x<8
2. -2x+12<-4
-2x+12-12<-4-12
-2x<-16
-2x/-2>-16/-2
x>8
3. Because the numbers are positive when divided.
4. The inequality sign is reversed because the 2nd to last step is divided by by a negative number. (This is also the same for multiplication)
5. -7d+8>29
-7d+8-8>29-8
-7d/7>21/-7
d>-3
6.12-3b<9
12-12-3b<9-12
-3b/-3>-3/-3
b>1
7.z/7-6=>-5
z/7-6+6=>-5+6
z/7*7=>1*7
z=>7 (what grade are you in?!)
When solving for a variable, you get the variable you're trying to solve for on one side and everything to the opposite of that variable.
We have the equation <span>5w + 9z = 2z + 3w.
Usually the variable we're solving for we want on the left. But it's fine to have it on the right side, too.
Let's subtract 9z from the left-hand side. That way, the 5w will be alone on the left-hand side.
And remember, anything we do on one side we do to the other side.
</span><span>5w + 9z - 9z = 2z + 3w - 9z
</span><span>5w = -7z + 3w
The 3w term on the right-hand side needs to be removed. So, subtract each side by 3w.
5w - 3w = -7z + 3w - 3w
2w = -7z
Now, we need to divide each side by 2 to see what the w variable is equal to.
2w / 2 = -7z / 2
w = -7z / 2 or w = -3.5z
So, w is equal to -3.5z.
</span>
Answer:
-2
Step-by-step explanation:
(-3x/2) - 3 = 3
add 3 to both sides
(-3x/2) = 3
multiply both sides by 2
-3x = 6
divide both sides by -3
x= -2
THE ANSWER IS D
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Answer:
The answer is C
Step-by-step explanation:
Use the Pythagoras theorem which states that a2 = b2 + c 2
For easier understanding imagine a straight line along the x axis. At (0,0) we have Atlanta. Moving 21 units to our right we have Columbia. This is represented on the coordinate system by (21, 0). To go from Colombia to Charleston, which is located at (24, -11), we need to travel 3 units right along the x- axis to reach ‘24’ and ‘11’ units down along the y- axis to reach (24, -11). Starting from Colombia we can make an imaginary triangle with its perpendicular being the y- component and its base being the x- component, which as we have stated above is ‘-11’ and ‘3’ respectively
Now applying the Pythagoras theorem to calculate the hypothesis and hence the distance between Colombia and Charleston.
a, which represents the distance between Colombia and Charleston would be
a² = b² + c²
a² = (3)² + (-11)²
a = √[(3)² + (-11)²]
Hence the answer is C