Answer:
[tex]x =-\frac{41}{4}[/tex]
or
[tex]x =-10\frac{1}{4}[/tex]
Step-by-step explanation:
Given:
The given expression is.
[tex]1\frac{3}{4}+16+... = 7\frac{1}{2}[/tex]
Let x be the blank space.
[tex]1\frac{3}{4}+16+x = 7\frac{1}{2}[/tex]
Now we solve the given equation for x.
[tex]1\frac{3}{4}+16+x = 7\frac{1}{2}[/tex]
Now we substitute [tex]1\frac{3}{4}=1+\frac{3}{4}=\frac{4+3}{4}=\frac{7}{4}[/tex] Simlarly [tex]7\frac{1}{2}=\frac{15}{2}[/tex]in above equation.
[tex]\frac{7}{4}+16+x = \frac{15}{2}[/tex]
[tex]x = \frac{15}{2}-\frac{7}{4}-16[/tex]
[tex]x = \frac{15\times 2 - 7 - 16\times 4}{4}[/tex]
[tex]x = \frac{30 - 7 - 64}{4}[/tex]
[tex]x = \frac{30 - 71}{4}[/tex]
[tex]x =-\frac{41}{4}[/tex]
or
[tex]x =-10\frac{1}{4}[/tex]
Therefore the value of blank space is [tex]-\frac{41}{4}[/tex] or [tex]-10\frac{1}{4}[/tex]
