Question

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

Answer 1

you have to simplify your relation first:
\[ 5(x + 2) \ge 7x + 2(x - 1)\]
distribute the 5 on the left side (that means multiply 5 times each term inside the parens)
and distribute the 2 on the right side. You get:
\[ 5x+10 \ge 7x+2x-2 \]
on the right side you have 7 x's add 2 more x's. that is 9x's
\[ 5x+10 \ge 9x-2 \]
now add -5x to both sides
\[ 5x-5x+10 \ge 9x-5x-2 \]

Answer 2

that simplifies to
\[ 10 \ge 4x-2 \]
add 2 to both sides to get
\[ 12 \ge 4 x \]
finally , divide both sides by 4
\[ 3 \ge x \]
or
\[ x \le 3 \]
which means the same thing

Answer 3

I guess if we just read the 4 choices, we could figure out that 3 of them mean the same thing.

the one we *do not* want is the one that shows x is bigger than 3
(in other words we do not want to shade numbers bigger than 3)

Answer 4

so than b would be the answer right? @phi

Answer 5

@Michele_Laino

Answer 6

@welshfella