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Stella [2.4K]
2 years ago
14

-1/2x + 6 < 4x - 3 i need to find the value of X with step-by-step explanation

Mathematics
2 answers:
Ray Of Light [21]2 years ago
8 0

Answer:

\boxed{\boxed{\tt x>2}}

Step-by-step explanation:

\tt -\cfrac{1}{2}x+6

<u>Subtract 6 from both sides:</u>

  • <u />\tt -\cfrac{1}{2}x+6-6<u />
  • <u />\tt -\cfrac{1}{2}x<u />

<u>Now, subtract 4x from both sides:</u>

  • <u />\tt -\cfrac{1}{2}x-4x<u />
  • <u />\tt -\cfrac{9}{2}x<u />

<u>Multiply both sides by -1:</u>

  • <u />\tt -\cfrac{9}{2}x\times -1<u />
  • <u />\tt \cfrac{9}{2}x>9<u />

<u>Multiply both sides by 2:</u>

  • <u />\tt 2\times \cfrac{9}{2}x>9\times \:2<u />
  • <u />\tt 9x>18<u />

<u>Divide both sides by 9:</u>

  • <u />\tt \cfrac{9x}{9}>\cfrac{18}{9}<u />
  • <u />\tt x>2<u />

<u>____________________________</u>

WITCHER [35]2 years ago
7 0

Answer:

x > 2

Step-by-step explanation:

-1/2x + 6 < 4x - 3

Start by adding 1/2x to both sides to get both x's on the same side

6 < 4 1/2x - 3

Add 3 to both sides to keep the x's by themselves on one side

9 < 4 1/2x

Divide both sides by 4 1/2 to get x by itself

2 < x  so x > 2

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Answer:

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Step-by-step explanation:

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2 years ago
A sign standing 6 feet tall is situated 18 feet away from a flag pole. at a certain time of day the sign's shadow is 3 feet long
alexdok [17]
Observe attached picture.

On picture we have:
A = height of flagpole = x ft
B = length of flagpole's shadow = 24 ft
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D = length of sign's shadow = 3 ft

When we draw a picture representing this problem we can also add another line marked in red. This way we can see that we have two right-angle triangles. We can see that both have same angle marked with α.

We can apply trigonometry rules to find height of flagpole.

From small triangle containing sign we can find tangens function:
tan \alpha = \frac{C}{D}
Similarly we can do for large triangle containing flagpole:
tan \alpha = \frac{A}{B}

We see that these two equations have same left sides. This means that their right sides must also be same:
\frac{C}{D} = \frac{A}{B}
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Height of flagpole is 48 feet.

8 0
3 years ago
Area of triangle with following verticies (0,-9), (3,-9), and (0,-2)
Neporo4naja [7]

Answer:

Area = 21/2 = 10.5 area units

Step-by-step explanation:

Two of the points are on the same line (the y-axis) as they both have x-coordinates of 0. This can thus be the base of your triangle.

Two more are on the same line (y= -9) as they both have the same y-coordinate of -9. This can be the height of your triangle.

So you have a base which is between -2 and -9 (7 units) and a height which is between 0 and 3 (3 units) so now just use the equation for area of a triangle A=0.5*b*h

8 0
3 years ago
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3 years ago
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A1=1 , an= 4a n-1 -1
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<span>for part (a) find the sum of the first n terms of the arithmetic series. for part (b) find n for the given sum Sn.
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