Question

Medal and Fan

A set of numbers is shown below:

{0, 0.6, 2, 4, 6}

Which of the following shows all the numbers from the set that make the inequality 2x + 3 ≥ 7 true?

{4, 6}
{0, 0.6, 2}
{0, 0.6}
{2, 4, 6}

Answer 1

Go through the set of numbers 0, 0.6, 2, 4 and 6 one by one.

Let's start with the first value: 0

Replace every copy of x with 0 and simplify

\[\Large 2x+3 \ge 7\]
\[\Large 2*0+3 \ge 7\]
\[\Large 0+3 \ge 7\]
\[\Large 3 \ge 7\]

The inequality \(\Large 3 \ge 7\) is false, so the first inequality is false when \(\Large x=0\).

So 0 is NOT part of the solution set.

Answer 2

Do the same for the other values in the set given to you. Tell me what you get.

Answer 3

You can also solve the inequality, and then see which numbers from the set are part of the solution.

\(\large 2x + 3 \ge 7\)

Subtract 3 from both sides:

\(\large 2x \ge 4\)

Divide both sides by 2:

\(\large x \ge 2\)

Now you need to pick the set out of the choices that contains all numbers from the original set that satisfy the solution of the inequality.

Check each number in \(x \ge 2\).
The ones that work are part of the solution set.