Question

Please help me with this problem im confused.

Answer 1

Answer: A. D.

Explanation:

A.

x-b-3<0

x-b-3+3<0+3

x-b<3 (yes)

B.

0>b-x+3

0+x>b-x+3+x

x>b+3

x-b>b+3-b

x-b>3 (no)

C.

x<3-b

x+b<3-b+b

x+b<3 (no)

D.

-3<b-x

-3+3<b-x+3

0<b-x+3

0+x<b-x+3+x

x<b+3

x-b<b+3-b

x-b<3 (yes)

Answer 2

A and D

Explanation:

Option A

`\begin{aligned}& \textsf{Given inequality}: & x-b-3 & < 0\\& \textsf{Add 3 to both side}: \quad & x-b-3+3 & < 0+3\\& \textsf{Simplify}: & x-b & < 3\end{aligned}`

Option B

`\begin{aligned}& \textsf{Given inequality}: & 0 & > b-x+3\\& \textsf{Add $x$ to both sides}: & 0+x & > b-x+3+x\\& \textsf{Simplify}: & x & > b+3\\& \textsf{Subtract $b$ from both sides}: \quad& x-b & > b+3-b\\& \textsf{Simplify}: & x-b & > 3\end{aligned}`

Option C

`\begin{aligned}& \textsf{Given inequality}: & x & < 3-b\\& \textsf{Add b to both sides}: \quad & x+b & < 3-b+b\\& \textsf{Simplify}: & x+b & < 3\end{aligned}`

Option D

`\begin{aligned}& \textsf{Given inequality}: & -3 & < b - x\\& \textsf{Divide both sides by -1}: \quad & (-3)/(-1) & > (b)/(-1)-(x)/(-1)\\& \textsf{Simplify}: & 3 & > -b+x\\& \textsf{Simplify}: & x-b & < 3\end{aligned}`

Note: When multiplying or dividing by a negative number in an inequality, remember to flip the inequality sign.