Question

HELP ME PLEASE I NEED HELP​

Answer 1

Answer:  -11 < x < -4

x is some number between -11 and -4; x cannot equal -11, x cannot equal -4.

the graph on the number line will show two open circles at -11 and -4 with shading between the two open circles (the open circles are not filled in).

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Work Shown on how I got that answer:

2 - |(2/5)*x + 3| > 3/5

2 - |(2/5)*x + 3| - 2 > 3/5 - 2 ... see note 1 (below)

-|(2/5)*x + 3| > 3/5 - 10/5 ... see note 2

-|(2/5)*x + 3| > -7/5

|(2/5)*x + 3| < 7/5 ... see note 3

-7/5 < (2/5)*x + 3 < 7/5 ... see note 4

5*(-7/5) < 5*( (2/5)*x + 3 ) < 5*(7/5) ... see note 5

-7 < 5*(2/5)*x + 5*3 < 7

-7 < 2x + 15 < 7

-7-15 < 2x + 15-15 < 7-15 ... see note 6

-22 < 2x < -8

-22/2 < 2x/2 < -8/2 ... see note 7

-11 < x < -4

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notes:

• note 1: I subtracted 2 from both sides
• note 2: We can write "2" as "10/5" since 10/5 = 2, this helps us combine the fractions on the next step.
• note 3: I multiplied both sides by -1. This will flip the inequality sign.
• note 4: Use the rule that if |x| < k, then -k < x < k for some positive number k.
• note 5: Multiply all three sides by 5 so the denominators of 5 cancel out (ie the fractions go away).
• note 6: Subtract 15 from all three sides to undo the +15 in the middle.
• note 7: Divide all three sides by 2 to undo the "multiplication of 2" done on the x. This fully isolates x.

Answer 2

Step-by-step explanation:

You should prolly subtract 2 from both sides first.

So you get, -|2/5x + 3| > -1 2/5

• Add three to both sides
• -|2/5x| = -1 2/5
• Do -1 and 2/5 divided by 2/5 to get -3.5, x > -3.5

One of the answers is x > -3.5 but you need to switch the sign to less than and make the other side the opposite.

$-( \frac{2}{5}x + 3 ) < 1 \frac{2}{5}$

You see that, switched the sign and made whats on the right side opposite. So now solve for x again but with this new equation. Also, the parentheses are absolute value signs

Subtract 3 from both sides

-|2/5x| < -1 and 3/5

Divide 2/5 from each side to get x < -4

I hope I'm correct, my bad if I'm wrong