2 years ago

If -2x +7 = 3x - 8, then x =

1 answer:

6 0

-2x +7 = 3x - 8

Move the variable to the left-hand side and change its sign

-2x -3x+ 7 = -8

Move the constant to the right-hand side and change its sign

-2x -3x = -8 -7

Collect like terms

-5x = -15

Divide both sides of the equation by -5

x=3

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1 year ago

Write the absolute value inequality in the form Ix−bIc that has the solution set x≤−9 or x≥−5.

Valentin [98]

Answer:

$\large\boxed{|x+7|\geq2}$

Step-by-step explanation:

Look at the picture.

$|x-a|\geq b\\\\a=\dfrac{-9+(-5)}{2}=\dfrac{-14}{2}=-7\\\\b=-9-(-7)=-9+7=-2\\b=-5-(-7)=-5+7=2\\\\|x-(-7)|\geq2\\\\|x+7|\geq2\\\\Check:\\\\|x+7|\geq2\iff x+7\geq2\ \vee\ x+7\leq-2\qquad\text{subtract 7 from both sides}\\\\x+7-7\geq2-7\ \vee\ x+7-7\leq-2-7\\\\x\geq-5\ \vee\ x\leq-9\qquad CORRECT\ :)$