How do you write an inequality and solve given "three fourths of a number decreased by nine is at least forty two"?

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How do you write an inequality and solve given &quot;three fourths of a number decreased by nine is at least forty two&quot;?

tennispopj8 · Accepted Answer

Step 1First, let&#039;s call &quot;a number&quot;       n  &quot;three fourths of a number&quot; then can be written as:            3      4        n  This, &quot;decreased by nine&quot; then can be written as:            3      4        n    -    9  &quot;is at least&quot; is the same as       ≥   so we can now write:            3      4        n    -    9    ≥  and what it is &quot;at least&quot; is &quot;forty two&quot; so:            3      4        n    -    9    ≥    42  To solve this we first add                     9             to each side of the inequality to isolate the n term while keeping the inequality balanced:            3      4        n    -    9    +                  9              ≥    42    +                  9                        3      4        n    -    0    ≥    51              3      4        n    ≥    51  Now, we multiply each side of the inequality by                               4                                      3                     tosolve for n while keeping the inequality balanced:                              4                                      3                      ×          3      4        n    ≥                            4                                      3                      ×    51                                                          4                                                                                      3                                            ×                                                                                        3                                                                                                                                                      4                                                                          n    ≥                  4              ×    17        n    ≥    68

Taniyah Estrada · Accepted Answer

Step 1Let&#039;s use some punctuation so show exactly what is meant: note how the placement of a comma gives a different meaning.                              three fourths of a number                      ,                                       decreased by 9                                                         is at least 42                    Let the number be x                              3          4                x                            -        9                            ≥        42            Solving gives:            3      4        x    ≥    51              4      3        ×          3      4        x    ≥    51    ×          4      3            x    ≥    56  However, if we interpret it differently we could have:                              three fourths of,                                                          a number decreased by 9,                                                         is at least 42                                                  3          4                                              (          x          -          9          )                                    ≥        42            Solving gives:            4      3        ×          3      4              (      x      -      9      )        ≥    42    ×          4      3            x    -    9    ≥    56        x    ≥    65

How do you write an inequality and solve given "three

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