Question

−9x+2>18 AND 13x+15≤−4

Answer 1

Isolate the x. Do the opposite of PEMDAS.

-9x + 2 > 18

Subtract 2 from both sides

-9x + 2 (-2) > 18 (-2)

-9x > 18 - 2

-9x > 16

Isolate the x. Divide -9 from both sides. Note that when dividing by a negative number, you must flip the sign.

(-9x)/-9 > (16)/-9

x < 16/-9

x < -1.78 (rounded)

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13x + 15 ≤ -4

Do the same for this one. First, subtract 15 from both sides

13x + 15 (-15) ≤ -4 (-15)

13x ≤ - 19

Divide 13 from both sides

13x/13 ≤ -19/13

x ≤ -19/13

x ≤ ~-1.46 (rounded)

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hope this helps

Answer 2

Solution for the given compound inequality is

$x<-\frac{16}{9}$

Given :

Given inequality

$-9x+2>18\; and \; 13x+15\leq -4$

Solve the inequality one by one

Lets break the inequality and solve it

$-9x+2>18\\-9x>18-2\\-9x>16\\Divide \; by \; -9\\x<\frac{-16}{9}$

Now we solve second inequality

$13x+15\leq -4\\13x\leq -4-15\\13x\leq -19\\x\leq \frac{-19}{13}$

Now we combine both solutions

Merge overlapping intervals

$x<-\frac{16}{9}\quad \mathrm{and}\quad \:x\le \:-\frac{19}{13}\\x<-\frac{16}{9}$

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