The algebraic expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)
Solution:
Given the statement:
Three sets of a sum of a number and four are added to the sum of seven times the same number and thirteen
Let us first understand the given statement,
Let the number be "x"
" sum of a number and four" means x + 4
"Three sets of a sum of a number and four" translated to 3(x + 4)
"sum of seven times the same number and thirteen" means 7x + 13
Thus the algebraic expression for given statement is:
[tex]3(x+4)+(7x + 13)[/tex]
Using distributive property in above expression
[tex]a(b+c) = ab + bc[/tex]
Therefore,
[tex]3(x+4)+(7x + 13) = 3x + 12 + 7x + 13[/tex]
Combine the like terms
[tex]3(x+4)+(7x + 13) = 10x+25[/tex]
Thus the required expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)
