Question

(repost) Please help! It involves inequalities! Also please include a number line.

Answer 1

Answer:

  -5 ≤ x

Step-by-step explanation:

2(x -3) -5x ≤ 9 . . . . . given

2x -6 -5x ≤ 9 . . . . . . eliminate parentheses

-3x -6 ≤ 9 . . . . . . . . combine like terms

-6 ≤ 9 +3x . . . . . . . add 3x

-15 ≤ 3x . . . . . . . . subtract 9

-5 ≤ x . . . . . . . . . divide by 3

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The point x=-5 is included in the solution set, so there is a sold dot at that point. The rest of the solution set is values of x that are greater than that value, so the number line is shaded to the right of that point. Your number line should show an arrow at the right end of the graph to indicate it extends that direction indefinitely. (My graphing program doesn't draw arrows easily.)

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Additional comment

Perhaps the most straightforward way to solve this would have been to add 6 instead of 3x. That would give ...

  -3x ≤ 15

Then dividing by -3 would give x. That operation would reverse the inequality symbol (because the divisor is negative). Then you would have ...

  x ≥ -5

Either way works. We judge it to be less confusing when we don't have to change the direction of the inequality symbol.