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djyliett [7]
3 years ago
14

Solve the inequality: −1<|2 x − 3|<7

Mathematics
1 answer:
andriy [413]3 years ago
5 0

Answer:

Step-by-step explanation:

1. subtract over the x on the right side of the inequality so you get 4x<16  divide 4 over to get x alone the inequality turns into x<4.

2. subtract over the x on the right side so you get 11x<22 divide over 11 to get x<2  

3. Add over 10 to get -8x>7x+30 subtract over 7x to get -15x>30 divide by -15 to get x<-2 make sure to flip over the sign since you're dividing by a negative  

4. Add over the 4 to get 13x<12x+3 subtract over 12 and get x<3

5. I can't solve five since their is no inequality sign, the answers show it both ways so i need a starting one to go off on but it is either A or B just flip over the original sign and that will be the answer .

6. Distribute the 7 to get 7x-14<-5 add over the 14 and get 7x<9 divide over the 7 and get x<9/7

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4. Determine the following difference. (2x² + 3x - 10) - (x² - x + 111)  please explain
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Hi there! The answer is A.

(2x² + 3x - 10) - (x² - x + 111) 
Let's solve this problem step by step!

First work out the parenthesis. Because we multiply by negative 1, we mustn't forget to change the symbols in front of the factors.
2x² + 3x - 10 - x² + x - 111

Now rearrange our expression, in order to collect the terms later.
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\qquad \qquad\huge \underline{\boxed{\sf Answer}}

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d1i1m1o1n [39]

Answer:

The equations shows a difference of squares are:

<u>10y²- 4x²</u>   $   <u>6y²- x²</u>

Step-by-step explanation:

the difference of two squares is a squared number subtracted from another squared number, it has the general from Ax² - By²

We will check the options to find which shows a difference of squares.

1) 10y²- 4x²

The expression is similar to the general form, so the equation represents a difference of squares.

It can be factored as (√10 y + 2x )( √10 y - 2x)

2) 6y²- x²

The expression is similar to the general form, so the equation represents a difference of squares.

It can be factored as (√6y + x )( √6y - x)

3) 8x²−40x+25

The expression is not similar to the general form, so the equation does not represent a difference of squares.

4) 64x²-48x+9

The expression is not similar to the general form, so the equation does not represent a difference of squares.

6 0
3 years ago
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