Question 703167
Although it is not clear,
I assume you are listing parts of two different problems.
There must be clues, probably in a figure that goes with the problem.
I do not see the picture that must be part of the problems, so I can only guess.
I imagine there is a rectangle HIJK.
Maybe the angles are marked with little squares to indicate they are right angles,
or maybe there is something else that indicates HIJK is a a rectangle.
That would be the clue.
If HIJK is a rectangle, the lengths of diagonals HJ and IK are the same.
 
HJ = x and IK = 2x - 7 
If geometry tells you that the lengths of HJ and IK are the same, you could write
{{{2x-7=x}}} and that is now an algebra problem.
Subtract {{{x}}} from both sides of the equal sign to get {{{x-7=0}}}
Add {{{7}}} to both sides to get {{{highlight(x=7)}}}
 
HJ = 3x +5 and IK= 5x-9
If geometry tells you that the lengths of HJ and IK are the same, you could write
{{{5x-9=3x+5}}} and that is now an algebra problem.
Subtract {{{3x}}} from both sides of the equal sign to get {{{2x-9=5}}}
Add {{{9}}} to both sides to get {{{2x=14}}}
Divide both sides by {{{2}}} to get {{{highlight(x=7)}}}