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Please, please help me.

 May 9, 2018
 #1
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The inequality at step 3 is wrong.

 

\(\big(\frac44\big)\frac{x-3}{6}\)     does not equal     \(\frac{4x-3}{24}\)

 

\(\big(\frac44\big)\frac{x-3}{6}\)     does equal     \(\frac{4x-12}{24}\)

 

The student did not correctly distribute the  4  in the numerator.

 

The second error occurs at step 8. When both sides of an inequality are divided by a negative number, the inequality sign needs to be flipped.

 May 9, 2018
 #2
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7/24 - (x + 1)/8<=(x - 3)/6             multiply both sides by 24

7 - 3(x + 1) <= 4(x - 3)

7 - 3x - 3 <= 4x - 12                      add 3x to both sides

7 - 3 <= 7x - 12

4 <= 7x - 12                                   add 12 to both sides

16 <= 7x                                        divide both sides by 7

16/7 <= x, OR:

x >= 16/7

 May 9, 2018

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