Given:
3 times x plus 4 is greater than or equal to 4 times the sum of x and 1.
To find:
The inequality for the given statement and solution of the inequality.
Solution:
4 times the sum means a distributive property problem.
Now,
3 times x : 3x
3 times x plus 4 : 3x+4
Greater than or equal to : ≥
4 times the sum of x and 1 : 4(x+1)
So, the inequality is
[tex]3x+4\geq 4(x+1)[/tex]
Using distributive property, we get
[tex]3x+4\geq 4x+4[/tex]
Isolate variable terms.
[tex]4-4\geq 4x+3x[/tex]
[tex]0\geq x[/tex]
It can be written as
[tex]x\leq 0[/tex]
Therefore, the required inequality is [tex]3x+4\geq 4(x+1)[/tex] and the solution is [tex]x\leq 0[/tex].
