Answer:
47. [tex]x < 7[/tex] or [tex]x > -9[/tex]
50. [tex]x > 7[/tex] or [tex]x < 17[/tex]
53. [tex]x < \frac{-4}{3}[/tex] or [tex]x > \frac{32}{3}[/tex]
56. [tex]x > -28[/tex] or [tex]x < -52[/tex]
Step-by-step explanation:
47. [tex]| x + 1| < 8[/tex]
-There are two equations:
Equation 1:
[tex]x + 1 < 8[/tex]
or
Equation 2:
[tex]x + 1 > -8[/tex]
-Solving equation 1:
[tex]x + 1 < 8[/tex]
[tex]x + 1 - 1< 8 - 1[/tex]
[tex]x < 7[/tex]
-Solving equation 2:
[tex]x + 1 > -8[/tex]
[tex]x + 1 - 1 > -8 - 1[/tex]
[tex]x > -9[/tex]
Answers:
[tex]x < 7[/tex] or [tex]x > -9[/tex]
50. [tex]| x + 5 | > 12[/tex]
-There are two equations:
Equation 1:
[tex]x + 5 > 12[/tex]
or
Equation 2:
[tex]x + 5 < -12[/tex]
-Solving equation 1:
[tex]x + 5 > 12[/tex]
[tex]x + 5 - 5 > 12 - 5[/tex]
[tex]x > 7[/tex]
-Solving equation 2:
[tex]x + 5 < -12[/tex]
[tex]x + 5 - 5 < -12 - 5[/tex]
[tex]x < -17[/tex]
-Answers:
[tex]x > 7[/tex] or [tex]x < -17[/tex]
53. [tex]| 14 - 3x | > 18[/tex]
-There are two equations:
Equation 1:
[tex]14 - 3x > 18[/tex]
or
Equations 2:
[tex]14 - 3x < -18[/tex]
-Solving equation 1:
[tex]14 - 3x > 18[/tex]
[tex]14 - 14 - 3x > 18 -14[/tex]
[tex]-3x > 4[/tex]
[tex]\frac{-3x}{-3} > \frac{4}{-3}[/tex]
[tex]x < \frac{-4}{3}[/tex] (Inequality sign changed, because of dividing by a negative number)
-Solve equation 2:
[tex]14 - 3x < -18[/tex]
[tex]14 - 14 - 3x < -18 -14[/tex]
[tex]-3x < -32[/tex]
[tex]\frac{-3x}{-3} < \frac{-32}{-3}[/tex]
[tex]x > \frac{32}{3}[/tex] (Inequality sign changed, because of dividing by a negative number)
-Answers:
[tex]x < \frac{-4}{3}[/tex] or [tex]x > \frac{32}{3}[/tex]
56. [tex]| 20 + \frac{1}{2}x | > 6[/tex]
-Switch the equation:
[tex]| \frac{1}{2}x + 20 | > 6[/tex]
-There are two equations:
Equations 1:
[tex]\frac{1}{2}x + 20 > 6[/tex]
or
Equation 2:
[tex]\frac{1}{2}x + 20 < -6[/tex]
-Solving equation 1:
[tex]\frac{1}{2}x + 20 > 6[/tex]
[tex]\frac{1}{2}x + 20 - 20 > 6 - 20[/tex]
[tex]\frac{1}{2}x > -14[/tex]
[tex]2 \times \frac{1}{2}x > 2 \times -14[/tex]
[tex]x > -28[/tex]
-Solving equation 2:
[tex]\frac{1}{2}x + 20 < -6[/tex]
[tex]\frac{1}{2}x + 20 - 20 < -6 - 20[/tex]
[tex]\frac{1}{2}x < -26[/tex]
[tex]2 \times \frac{1}{2}x < 2 \times -26[/tex]
[tex]x < -52[/tex]
-Answers:
[tex]x > -28[/tex] or [tex]x < -52[/tex]
And were done.
