Question

Hey! I was wondering if someone could explain to me how solving two-step inequalities works. Thanks!

Answer 1

Ok, let me break it down for you.
Step 1, 20-6. That is 14. You need to do that because you need it for step 2
Step 2, Since you want to get something less than 20, you need to find out what could get you to 20. So, 14÷-2. The answer is -7. So, anything less than -7 could be the answer.

Answer?
x= anything more than -7. But just for a specific answer, Let's say 0. Because -2×0=0. 0+6=6. 6<20.
Done! :)))

Answer 2

Here is the inequality:

`-2x+6<20`

You're looking for x. To find it, you have to remove everything on the same side of the variable. The only thing with it is positive 6. To remove it, you have to do the opposite of it, which is -6, which is also the same as subtracting 6. Subtract 6 from both sides:

`-2x+6-6<20-6 \\-2x<14`

Now you have -2x. When you have a negative variable, the inequality sign changes. Change the sign:

`-2x<14 \rightarrow -2x>14`

You're looking for x alone. To leave x alone, you have divide both sides by -2 since the variable is -2x. Divide both sides by -2:

`-2x / -2 > 14 / -2 \\\\x>-7`

When dividing a negative number number by a positive or vice versa, the result is ALWAYS negative. That's why in your answer, it's -7.

Your answer is x > -7

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