Help to solve 2 questions (2x - 7)(x + 1) = 5 – x(1 – 2x) and (2x - 7)(x + 1) < 5 – x(1 – 2x)?

Question

Please show proper technique for me to accomplish this by myself next time, Thank You...

Answer 1

1.

(2x-7)(x+1) = 5-x(1-2x)

2x^2 - 7x + 2x - 7 = 5 -x + 2x^2 (multiply out brackets)

2x^2 -5x -7 = 5 -x +2x^2 (collect terms)

-5x - 7 =5 - x

-4x - 7 = 5

-4x = 12

x = -3

2.

(2x-7)(x+1) &lt; 5-x(1-2x)

2x^2 -7x +2x - 7 &lt; 5-x+2x^2 (multiply out brackets)

-4x &lt; 12  (collect terms)

now divide both sides by -1 (remembering to change direction of)

4x &gt; -12

x &gt; -3

Answer 2

I don&#039;t know how to write x squared ( x with the small 2 on top ) on the computer so i will use ^ between the x and the 2.

2X^2 + 2X - 7X - 7= 5 - X + 2X^2

-5X - 7 = 5 - X

-4X = 12

X = 12/-4

X = -3

2X^2 + 2X - 7X - 7 &lt; 5 - X +2X^2

-5X - 7 &lt; 5-X

-4X &lt; 12

X &gt; 12/-4

X &gt; -3

NOTICE: the sign changes when you divide by a negative number.

I didn&#039;t put all the step because I assume you have some knowledge of the problems and would understand. Also not knowing how to write the index is frustrating

Answer 3

Equation 1

(2x-7)(x+1)=5-x(1-2x)

2x^2 + (2x-7x) -7 =5-x + 2x^2

2x^2 -5x -7= 5- x + 2x^2

0 = 4x +12

-12 = 4x

-3 = x

the 2x^2 cancel out.

equation 2

the same but you just replace the &quot;=&quot;sign with &quot;&lt;&quot; sign so

-3 &lt; x or if you reverse it

3&gt;x

Answer 4

1.

  (2x - 7)(x+1) = 5-x(1 -2x)

  = 2x^2 - 5x -7 = 5 - x + 2x^2

  = 4x =  -12

  =  x = - 3

2.

   (2x - 7)(x + 1) &lt; 5 - x(1 - 2x)

  =2x^2 - 5x -7 &lt; 5 - x +2x^2

  =4x&lt;  - 12

  = x &lt; -3

  

Answer 5

hi

  1:  

  =&gt; 2(x)^2 +2x -7x -7 = 5-x+2(x)^2

                        2x-7x+x=5+7 ==&gt; -4x=12 ==&gt; x=-3

2:

=&gt; 2(x)^2+2x-7x-7&lt;5-x+2(x)^2

                  2x-7x+x &lt; 5+7

                  -4x   &lt;   12  

                   - x  &lt;  3

                     x  &gt;  -3

Answer 6

The way I would do this is to multiply out the brackets on both sides, so with the first one, you would get

2x(squared)-5x-7 = 2x(squared)-11x+5.  

To both sides, i would add 7, to cancel out the minus seven on the right,  so you get

2x(squared)-5x = 2x(squared)-11x+12.

Then i would add 5x to both sides, to cancel out the minus 5x on the right, so you get

2x(squared) = 2x(squared)-6x+12.

This means that -6x=12, to make the expression true.

Divide this by -6, and you get the answer,

x = -2.

As for the second one, it is the same process, just with a &lt; sign.

I hope this has helped you.  

Answer 7

(2x - 7)(x + 1) = 5 - x(1 - 2x)

2x^2 + 2x - 7x - 7 = 5 - x + 2x^2

2x^2 - 2x^2 - 5x + x - 7 - 5 = 0

-4x - 12 = 0

-4x = 12

x = 12/-4

x = -3

(2x - 7)(x + 1) &lt; 5 – x(1 – 2x)

2x^2 + 2x - 7x - 7 &lt; 5 - x + 2x^2

2x^2 - 2x^2 - 5x + x - 7 - 5 &lt; 0

-4x - 12 &lt; 0

-4x &lt; 12

4x &gt; -12

x &gt; -3