Solution of the equation: [tex]x=6\frac{1}{2}[/tex]
Step-by-step explanation:
The equation that we have to solve in this problem is:
[tex]13\frac{3}{4}+x=7\frac{1}{4}[/tex]
The first step to do is to rewrite the mixed fractions as improper fractions. We have:
[tex]13\frac{3}{4}=\frac{13\cdot 4+3}{4}=\frac{52+3}{4}=\frac{55}{4}[/tex]
And
[tex]7\frac{1}{4}=\frac{7\cdot 4+1}{4}=\frac{29}{4}[/tex]
So the equation becomes
[tex]\frac{29}{4}+x=\frac{55}{4}[/tex]
Now we multiply by 4 each term on both sides, and we get
[tex]29+4x=55[/tex]
Now we subtract 29 from both sides,
[tex]4x=55-29=26[/tex]
And finally, we divide both sides by 4:
[tex]x=\frac{26}{4}=\frac{13}{2}=6\frac{1}{2}[/tex]
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