Question

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 1

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

`3x+4\geq 4(x+1)`

Using distributive property, we get

`3x+4\geq 4x+4`

Isolate variable terms.

`4-4\geq 4x+3x`

`0\geq x`

It can be written as

`x\leq 0`

Therefore, the required inequality is
`3x+4\geq 4(x+1)` and the solution is
`x\leq 0`.