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Which of the following is not a way to represent the solution of the inequality 5(x + 2) greater than or equal to 7x + 2(x − 1)? . A number line with a closed circle on 3 and shading to the right. . A number line with a closed circle on 3 and shading to the left. . 3 greater than or equal to x . x less than or greater to 3

Verified Answer :

carlosego

For this case we have the following inequality:


\(5 (x + 2)\geq 7x + 2 (x - 1)
\)

We must rewrite the inequality to find the solution.

By doing distributive property we have:

\(5x + 10\geq7x + 2x - 2
\)

Adding similar terms we have:

\(5x + 10\geq 9x - 2
\)

Combining similar terms:

\(2 + 10\geq9x - 5x
\)

Rewriting we have:


\(12\geq 4x
\)

Clearing the value of x we have:


\(\frac{12}{4}\geq x
\)

\(3\geq x
\)

Therefore, the solution set is:

(-∞, 3]

Answer:

The following is not a way to represent the solution of the inequality:

A number line with a closed circle on 3 and shading to the right

Answer:

option: B is correct.

( A number line with a closed circle on 3 and shading to the left ).

Step-by-step explanation:

We are asked to find which  of the following is not a way to represent the solution of the inequality 5(x + 2) greater than or equal to 7x + 2(x − 1) i.e. we are given a inequality as:

\(5(x+2)\geq7x+2 (x-1)\)

i.e. \(5x+10\geq7x+2x-2\)

i.e. \(5x+10\geq9x-2\)

\(10+2\geq9x-5x\\\\12\geq4x\\\\x\leq3\)

Hence, the region in the number line is:

(-∞,3]

Hence, we get a number line with a closed circle at  3 and shaded region to the left of 3.

Hence Option B is correct.

( A number line with a closed circle on 3 and shading to the left ).

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