QUESTION A
The given inequality is
[tex]x-1\:>\:5[/tex]
Add 1 to both sides of the inequality to obtain;
[tex]x\:>\:5+1[/tex]
[tex]x\:>\:6[/tex]
Answer: 2. [tex]x\:>\:6[/tex], open dot at 6 and shaded to the right.(A)
QUESTION B.
The given inequality is [tex]2x \le 6[/tex].
Divide both sides by 2;
[tex]x \le \frac{6}{2}[/tex].
[tex]x \le 3[/tex].
Answer: 5. [tex]x \le 3[/tex], closed dot at 3 and shaded to the left(B).
QUESTION C
The given inequality is [tex]x-7\:>\:-4[/tex]
Add 7 to both sides to get;
[tex]x\:>\:-4+7[/tex]
[tex]\Rightarrow x\:>\:3[/tex]
Answer: 7. [tex]x\:>\:3[/tex], open dot at 3 and shaded to the right.(C)
QUESTION D
We want to solve;
[tex]-2x \:<\:6[/tex]
Divide through by -2 and reverse the inequality sign;
[tex]x \:>\:\frac{6}{-2}[/tex]
[tex]x \:>\:-3[/tex]
Answer; 3. [tex]x \:>\:-3[/tex] Open dot at -3 and shaded to the right. (D)
QUESTION E
We have
[tex]4\:<\:-4x[/tex]
Divide through by -4 and reverse the sign.
[tex]\frac{4}{-4}\:>\:x[/tex]
[tex]-1\:>\:x[/tex]
or
[tex]x\:<\:-1[/tex]
Answer: 6. [tex]x\:<\:-1[/tex] open dot at -1, and shaded to the left(E)
QUESTION F
The given inequality is [tex]-2x+3\:<\:-7[/tex]
Add -3 to both sides to get;
[tex]-2x\:<\:-7-3[/tex]
[tex]-2x\:<\:-10[/tex]
Divide both sides of the inequality by -2 and reverse the sign;
[tex]x\:>\:5[/tex]
Answer:9. [tex]x\:>\:5[/tex], open dot at 5 and shaded to the right(F)
QUESTION G
The given inequality is
[tex]5x+1\ge11[/tex]
[tex]5x\ge11-1[/tex]
[tex]5x\ge10[/tex]
Divide by 5
[tex]x\ge2[/tex]
Answer ; 10. [tex]x\ge2[/tex], closed dot at 2 and shaded to the right(G)
QUESTION H
We have [tex]3(x+4)\:>\:8x-6[/tex]
Expand the bracket to get;
[tex]3x+12\:>\:8x-6[/tex]
Group similar terms to get;
[tex]3x-8x\:>\:-6-12[/tex]
Simplify
[tex]-5x\:>\:-18[/tex]
Divide through by -5 and reverse the sign;
[tex]x\:<\:18/5[/tex]
Answer: 1. [tex]x\:<\:18/5[/tex] Open dot at 18/5 and shaded to the left(H)
QUESTION I
We have [tex]-3x+4\:<\:-x+2[/tex].
[tex]-3x+x\:<\:2-4[/tex]
[tex]-2x\:<\:-2[/tex]
Divide by -2 and reverse the sign;
[tex]x\:>\:1[/tex]
Answer: 8. [tex]x\:>\:1[/tex], open dot at 1 and shaded to the right(I)
J. The given inequality [tex]-2(x-4)\:>\:5-(x+2)[/tex]
Expand the bracket to get;
[tex]-2x+8\:>\:5-x-2[/tex]
Group like terms to get;
[tex]-2x+x\:>\:5-2-8[/tex]
[tex]-x\:>\:-5[/tex]
Divide by -1 and reverse the sign to get;
[tex]x\:<\:5[/tex]
Answer; 4. [tex]x\:<\:5[/tex], open dot at 5 and shaded to the left.(J)
