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;

$x \le \frac{6}{2}$.

$x \le 3$.

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;

$-2x \:$

Divide through by -2 and reverse the inequality sign;

$x \:>\:\frac{6}{-2}$

$x \:>\:-3$

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

QUESTION E

We have  

$4\:$

Divide through by -4 and reverse the sign.

$\frac{4}{-4}\:>\:x$

$-1\:>\:x$

or

$x\:$

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

QUESTION F

The given inequality is $-2x+3\:$

Add -3 to both sides to get;

$-2x\:$

$-2x\:$

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;

$x\:$

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

QUESTION I

We have $-3x+4\:$.

$-3x+x\:$

$-2x\:$

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;

$x\:$

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