Help me solve the Inequality Word Problem and solve ?
1 answer:
Let x represent the number
.. 1 +3x . . . . . . one more than three times a number
.. x -5 . . . . . . . the number decreased by 5
.. 1 +3x < x -5 . . . . the relation specified by the problem statement
.. 2x < -6 . . . . . . . subtract x+1
.. x < -3 . . . . . . . . . divide by the coefficient of x. (Positive, so < stays the same.)
.. 1 +3x . . . . . . one more than three times a number
.. x -5 . . . . . . . the number decreased by 5
.. 1 +3x < x -5 . . . . the relation specified by the problem statement
.. 2x < -6 . . . . . . . subtract x+1
.. x < -3 . . . . . . . . . divide by the coefficient of x. (Positive, so < stays the same.)
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We need to account for both x values on either side of the length, and width.
Thus, the length becomes 10 + x + x = 10 + 2x
and the width becomes 5 + x + x = 5 + 2x
For the second question, I'm assuming we don't account for the area that is covered by the garden.
Then we can say that the path is measured by: (5 + 2x)(10 + 2x) - 50, which is the area of the garden itself.
(5 + 2x)(10 + 2x) - 50 = 54
Expanding the brackets:
x = -9, or x = 3/2
Since x > 0, then x ≠ -9
Thus, the only x-value we can take is x = 3/2
Thus, the length becomes 10 + x + x = 10 + 2x
and the width becomes 5 + x + x = 5 + 2x
For the second question, I'm assuming we don't account for the area that is covered by the garden.
Then we can say that the path is measured by: (5 + 2x)(10 + 2x) - 50, which is the area of the garden itself.
(5 + 2x)(10 + 2x) - 50 = 54
Expanding the brackets:
x = -9, or x = 3/2
Since x > 0, then x ≠ -9
Thus, the only x-value we can take is x = 3/2