Question

Solve the inequality. 2(4+2x)≥5x+5
x≤−2
x≥−2
x≤3
x≥3

Answer 1

Option C.

Explanation:

The given inequality is given as

2(4 + 2x) ≥ 5x + 5

8 + 4x ≥ 5x + 5 [Simplify the parenthesis by distributive law]

Subtract 5 from each side of the inequality

(8 + 4x) - 5 ≥ (5x + 5) - 5

3 + 4x ≥ 5x

subtract 4x from each side of the inequality

(4x + 3) - 4x ≥ 5x - 4x

3 ≥ x

Or x ≤ 3

Option C. x ≤ 3 is the correct option.

Answer 2

The solution of the inequality is:

`x\leq 3`

Explanation:

We are given a inequality in terms of variable x as:

`2(4+2x)\geq 5x+5`

Now we are asked to find the solution of the inequality i.e. we are asked to find the possible values of x such that the inequality holds true.

We may simplify this inequality as follows:

On using the distributive property of multiplication in the left hand side of the inequality we have:

`2* 4+2* 2x\geq 5x+5\\\\i.e.\\\\8+4x\geq 5x+5\\\\i.e.\\\\8-5\geq 5x-4x\\\\i.e.\\\\x\leq 3`

The solution is:
`x\leq 3`