We have two responses for you
Let me illustrate with a similar problem.
You can solve an inequality as you would solve an equality (equation) with one change. If you multiply or divide both sides of the inequality by a negative number, the direction of the inequality reverses. In my problem, as in yours, there are two inequalities, -6 < 4 - 5x and 4 - 5x ≤ 9 but if you are careful you can solve both at the same time.
The object is to manipulate the inequalities and end with a statement of the form
where the inequalities may be ≤. So I start with
First I add -4 to both sides of each inequality to get
I don't want the negative sign between the inequalities so I multiply through by -1. Since -1 is negative this reverses the direction of the inequalities.
Since the number line is arranged so that larger numbers are to the right you might find it more natural to write this
The final step is to divide through by 5 to get
Now try your problem,
Helen, to answer these questions, you simply treat it like an equation
Here's an example:
20 > 7-4x > 4
I want x by itself in the middle, so first I subtract 7 from all sides:
Now I divide all sides by -4. I have to flip the direction of the
So x is between -13/4 and 3/4. I can write this as (-13/4, 3/4)
Now you try it with -1 < 5-2x < 10.
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