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3 times x plus 4 is greater than or equal to 4 times the sum of x and 1. (Hint: 4 times the sum means you should write a distributive property problem)

Answer :

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].

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