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Vinvika [58]
3 years ago
8

Solve the inequality x-4 < - 3.Then graph the solution set.show your work.

Mathematics
1 answer:
bearhunter [10]3 years ago
8 0

Answer:

x < 1

Step-by-step explanation:

x - 4 < - 3

<u>  + 4    +4</u>                        Do inverse operations by adding 4 on both sides

    x < 1

Therefore, the answer is x < 1.

(It isn't allowing me to attach a photo but I am just going to try make a visual of the graph below)

<------------------------------o------------------>

-4    -3    -2    -1     0    1     2    3      4

The circle is open because based on the concept that in inequalities, <em>less/greater than and/or equal to (such as these ≥ ≤ )</em> signs are graphed with closed circles, while less/greater than (like these > <) signs are graphed with open circles. The direction of the arrow is moving to the left on the number line because all possible values for x would be less than 1. When graphing the inequality you would use a solid line rather than a dashed line (I had to improvise since I could not attach an image).

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What is an equation of the line that passes through the point (−6,−1) and is perpendicular to the line 6x−y=7?
user100 [1]

Answer:

y=-1/6x-2

Step-by-step explanation:

Lets find the slope of the given line

6x-7=y,m=6

The slope of the perpendicular line would be=-1/6

Using the point-slope form y-y1=m(x-x1)

y--1=-1/6(x--6)

y+1=-1/6(x+6)

6y+6=-x-6

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3 years ago
For numbers 14a-14d , tell which expressions require you to rename mixed numbers before you can subtract. Find each difference.
ExtremeBDS [4]

Answer:

14b and 14d require renaming mixed numbers; 14a) 3 3/20; 14b) 2 1/8; 14c) 1 13/24; 14d) 3 3/6 = 3 1/2

Step-by-step explanation:

14a) First we find the least common denominator (LCD).  The first thing that both 5 and 4 will divide into is 20; this is our LCD.

It takes 4 5's to make 20; multiplying the numerator by 4, we have 5 8/20.  It takes 5 4's to make 20; multiplying the numerator by 5, we have 2 5/20.  Subtracting these,

5 8/20 - 2 5/20 = 3 3/20

14b) We must write the whole number 5 as a mixed number with a denominator of 8; 5 = 4 8/8.  This gives us

4 8/8 - 2 7/8 = 2 1/8

14c) The LCD of 3 and 8 is 24.  It takes 8 3's to make 24; multiplying the numerator by 8, we have 7 16/24.  It takes 3 8's to make 24; multiplying the numerator by 3, we have 6 3/24.  Subtracting we have

7 16/24 - 6 3/24 = 1 13/24.

14d) The LCD of 6 and 3 is 6.  Since the first mixed number has a denominator of 6, we leave it:  9 1/6.  It takes 2 3's to make 6; multiplying the numerator by 2, we have 5 4/6.  Subtracting we would have

9 1/6 - 5 4/6

We are subtracting a larger fraction from a smaller one.  This means we borrow a whole from the whole number, making it 8; this makes the fraction (6+1)/6 = 7/6.  This gives us

8 7/6 - 5 4/6 = 3 3/6 = 3 1/2

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