Question

Please help! I dont understand! Thank you

Answer 1

QUESTION A

The given inequality is

`x-1\:>\:5`

Add 1 to both sides of the inequality to obtain;

`x\:>\:5+1`

`x\:>\:6`

Answer: 2.
`x\:>\:6`, open dot at 6 and shaded to the right.(A)

QUESTION B.

The given inequality is
`2x \le 6`.

Divide both sides by 2;

`x \le (6)/(2)`.

`x \le 3`.

Answer: 5.
`x \le 3`, closed dot at 3 and shaded to the left(B).

QUESTION C

The given inequality is
`x-7\:>\:-4`

Add 7 to both sides to get;

`x\:>\:-4+7`

`\Rightarrow x\:>\:3`

Answer: 7.
`x\:>\:3`, open dot at 3 and shaded to the right.(C)

QUESTION D

We want to solve;

`-2x \:<\:6`

Divide through by -2 and reverse the inequality sign;

`x \:>\:(6)/(-2)`

`x \:>\:-3`

Answer; 3.
`x \:>\:-3` Open dot at -3 and shaded to the right. (D)

QUESTION E

We have

`4\:<\:-4x`

Divide through by -4 and reverse the sign.

`(4)/(-4)\:>\:x`

`-1\:>\:x`

or

`x\:<\:-1`

Answer: 6.
`x\:<\:-1` open dot at -1, and shaded to the left(E)

QUESTION F

The given inequality is
`-2x+3\:<\:-7`

Add -3 to both sides to get;

`-2x\:<\:-7-3`

`-2x\:<\:-10`

Divide both sides of the inequality by -2 and reverse the sign;

`x\:>\:5`

Answer:9.
`x\:>\:5`, open dot at 5 and shaded to the right(F)

QUESTION G

The given inequality is

`5x+1\ge11`

`5x\ge11-1`

`5x\ge10`

Divide by 5

`x\ge2`

Answer ; 10.
`x\ge2`, closed dot at 2 and shaded to the right(G)

QUESTION H

We have
`3(x+4)\:>\:8x-6`

Expand the bracket to get;

`3x+12\:>\:8x-6`

Group similar terms to get;

`3x-8x\:>\:-6-12`

Simplify

`-5x\:>\:-18`

Divide through by -5 and reverse the sign;

`x\:<\:18/5`

Answer: 1.
`x\:<\:18/5` Open dot at 18/5 and shaded to the left(H)

QUESTION I

We have
`-3x+4\:<\:-x+2`.

`-3x+x\:<\:2-4`

`-2x\:<\:-2`

Divide by -2 and reverse the sign;

`x\:>\:1`

Answer: 8.
`x\:>\:1`, open dot at 1 and shaded to the right(I)

J. The given inequality
`-2(x-4)\:>\:5-(x+2)`

Expand the bracket to get;

`-2x+8\:>\:5-x-2`

Group like terms to get;

`-2x+x\:>\:5-2-8`

`-x\:>\:-5`

Divide by -1 and reverse the sign to get;

`x\:<\:5`

Answer; 4.
`x\:<\:5`, open dot at 5 and shaded to the left.(J)