Question

5) give one solution to the inequality
12x-3x+11<4x-(17-9x).

6) explain why the equation 6|x|+22=4 has no solution.

isn't it because the x can't be there by itself. or because x and y-value both make the equation true

Answer 1

5 )

12 x - 3 x + 11 < 4 x - ( 17 - 9 x )

12 x - 3 x + 11 < 4 x - 17 + 9 x

9 x + 11 < 13 x - 17 Subtract 11 to both sides

9 x + 11 - 11 < 13 x - 17 - 11

9 x < 13 x - 28 Subtract 13 x to both sides

9 x - 13 x < 13 x - 28 - 13 x

- 4 x < - 28 Divide both sides by - 4

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Remark :

When you multiply or divide left and right sides of inequality WITH NEGATIVE NUMBER , you MUST CHANGE the direction of the inequality.
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- 4 x / -4 > - 28 / - 4

x > 7


6 )

6 abs ( x ) + 22 = 4 Subtract 22 to both sides

6 abs ( x ) + 22 - 22 = 4 - 22

6 abs ( x ) = - 18 Divide both sides by 6

6 abs ( x ) / 6 = - 18 / 6

abs ( x ) = - 3

That is not correct becouse the absolute value of a number is always positive.

That's why your equation has no solution.