The number of integers that satisfies the inequalities, -5 ≥ -7•x and -15 ≥ 5•x is zero or non
How can the inequalities be simplified?
The given inequalities are;
-5 ≥ -7•x and -15 ≥ 5•x
Simplifying the inequalities gives;
-5 ≥ -7•x
Dividing both sides by -7 gives;
-5/-7 ≤ -7•x/-7 = x
Therefore;
5/7 ≤ x
Which gives;
The second inequality is simplified as follows;
-15 ≥ 5•x
-15/5 ≥ 5•x/5
-3 ≥ x
Which gives;
x ≤ -3
Therefore;
-3 ≥ x and x ≥ 5/7
5/7 ≤ x ≤ -3
However, 5/7 > -3
The number of integers that satisfies the inequality, 5/7 ≤ x ≤ -3, is zero (no integer satisfies the inequality).
Therefore;
Non of the integers satisfies both -5 ≥ -7•x and -15 ≥ 5•x
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