The steps for solving the equation 2x-3=7 are listed below

x=5

Step-by-step explanation:

To solve this equation, we need to find out what the variable, x, is equal to. In order to do this, we need to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind that everything must be done to both sides.

2x-3=7

3 is being subtracted from 2x. The opposite of subtraction is addition. Add 3 to both sides

2x-3+3=7+3

2x=7+3

2x=10

x is being multiplied by 2. The opposite of multiplication is division . Divide both sides by 2.

2x/2=10/2

x=10/2

x=5

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12