Question

How to solve and answer, pls and thx​

Answer 1

D

Explanation:

first of all we need to solve the inequalities

`3-x\geq 2\\\\3-x+x\geq 2+x\\\\3\geq2+x \\\\3-2\geq 2-2+x\\\\1\geq x\\\\x\leq 1` (-∞,1] or ]-∞,1]

the second inequality is

`4x+2\geq 10\\\\4x+2-2\geq 10-2\\\\4x\geq 8\\\\(4x)/(4)\geq (8)/(4) \\\\x\geq 2` [2,∞) or [2,∞[

so the answer is D

Answer 2

Answer: D

Explanation:

To graph the inequalities on the number line, let's first solve them.

3-x≥2 [subtract both sides by 3]

-x≥-1 [divide both sides by -1, remember to flip inequalities]

x≤1

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4x+2≥10 [subtract both sides by 2]

4x≥8 [divide both sides by 4]

x≥2

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Now, we have our inequalities, x≤1 and x≥2. Notice that both inequalities are greater/less than or equal to. The "or equal to" part means that x is equal to 1 and 2. Therefore, when graphed, it is a closed circle. This let's us automatically eliminate B and C because they have open circles.

For x≤1, we know that x is going to be 1 and below, meaning it starts at 1 and travels left where it gets smaller and smaller. This tells us that the answer is D, but let's check to be sure.

For x≥2, we know that x is going to be greater than 2. This let's us know that the arrow will be pointing to the right, where the numbers are getting bigger and bigger. Knowing this, we can confirm that D is the correct answer.