Question

Which of the following is not a way to represent the solution of the inequality 2(x− 1) ≤ 10?

A. x ≤ 6
B. 6 ≥ x
C. A number line with a closed circle on 6 and shading to the left
D. A number line with a closed circle on 6 and shading to the right

Answer 1

Answer: The correct option is

(D) A number line with a closed circle on 6 and shading to the right.

Step-by-step explanation: We are given to select the correct option that is not a way to represent the solution of the following inequality:

`2(x-1)\leq 10~~~~~~~~~~~~~~~~~~~~~(i)`

First, we need to solve the inequality (i) for the value of x.

The solution is as follows:

`2(x-1)\leq 10\\\\\Rightarrow 2x-2\leq 10\\\\\Rightarrow 2x\leq 10+2\\\\\Rightarrow 2x\leq 12\\\\\Rightarrow x\leq 6\\\\\Rightarrow 6\geq x.`

So,
`x\leq 6` and
`6\geq x` are correct ways to represent the solution of inequality (i).

Also, since x is less than or equal to 6, so the solution contains all the real numbers which are less than 6 and also equal to 6.

So, there must be a closed circle on 6 shading to the left.

This implies that "A number line with a closed circle on 6 and shading to the left" is also a correct way to represent the solution.

The only incorrect way is "A number line with a closed circle on 6 and shading to the right".

Since the solution contains numbers less than or equal to 6, so the number line cannot be shaded on the right of 6.

Thus, the correct option is (D).

Answer 2

Answer: D. A number line with a closed circle on 6 and shading to the right

Explanation:

Here, the given inequality,

2(x− 1) ≤ 10

2x - 2 ≤ 10

2x ≤ 10 + 2

2x ≤ 12

x ≤ 6 or 6 ≥ x

The value of x is all numbers less than 6 including 6.

⇒ A number line with a closed circle on 6 and shading to the left.

Thus, by the above explanation,

Only option D 'A number line with a closed circle on 6 and shading to the right' is not a way to represent the solution of the inequality.