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# What values of satisfy ?

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What values of  satisfy

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Guest Dec 14, 2014

#1
+17745
+5

1)  When x - 4 ≤ 0, then |x - 4| = -(x - 4) = -x + 4       (when x ≤ 4)

2)  When x - 4 ≥ 0, then |x - 4| = x - 4                          (when x ≥ 4)

3)  When x + 4 ≤ 0,  then |x + 4| = -(x + 4) = -x - 4    (when x ≤ -4)

4)  When x + 4 ≥ 0, then |x + 4| = x + 4                      (when x ≥ -4)

When x ≤ -4, use both lines 1 and 3 above:  |x - 4| + |x + 4| ≤ 10

--->    -x + 4 + -x - 4 ≤ 10

--->                      -2x ≤ 10

--->                         x ≥ -5                 --->      -5 ≤ x ≤ -4

When x ≥ -4 and x ≤ 4, use both lines 1 and 4 above:  |x - 4| + |x + 4| ≤ 10

--->            -x + 4 + x + 4  ≤ 10

--->                                  8 ≤ 10

Since 8 ≤ 10 for all values in this range   --->   -4 ≤ x ≤ 4

When x ≥ 4, use both lines 2 and 4 above:  |x - 4| + |x + 4| ≤ 10

--->           x - 4 + x + 4 ≤ 10

--->                           2x ≤ 10

--->                             x ≤ 5                 --->   4 ≤ x ≤ 5

Combining these three answer:  -5 ≤ x ≤ 5

geno3141  Dec 15, 2014
#1
+17745
+5

1)  When x - 4 ≤ 0, then |x - 4| = -(x - 4) = -x + 4       (when x ≤ 4)

2)  When x - 4 ≥ 0, then |x - 4| = x - 4                          (when x ≥ 4)

3)  When x + 4 ≤ 0,  then |x + 4| = -(x + 4) = -x - 4    (when x ≤ -4)

4)  When x + 4 ≥ 0, then |x + 4| = x + 4                      (when x ≥ -4)

When x ≤ -4, use both lines 1 and 3 above:  |x - 4| + |x + 4| ≤ 10

--->    -x + 4 + -x - 4 ≤ 10

--->                      -2x ≤ 10

--->                         x ≥ -5                 --->      -5 ≤ x ≤ -4

When x ≥ -4 and x ≤ 4, use both lines 1 and 4 above:  |x - 4| + |x + 4| ≤ 10

--->            -x + 4 + x + 4  ≤ 10

--->                                  8 ≤ 10

Since 8 ≤ 10 for all values in this range   --->   -4 ≤ x ≤ 4

When x ≥ 4, use both lines 2 and 4 above:  |x - 4| + |x + 4| ≤ 10

--->           x - 4 + x + 4 ≤ 10

--->                           2x ≤ 10

--->                             x ≤ 5                 --->   4 ≤ x ≤ 5

Combining these three answer:  -5 ≤ x ≤ 5

geno3141  Dec 15, 2014