a > 4 for which the solutions of the inequality are all real numbers.
Inequality
It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).
The solutions for inequalities can be given by: a graph in a number line or numbers.
For solving this exercise, it is necessary to find a for the given inequality.
a(x+3) < 5x+15-x
a(x+3) < 4x +15
ax+3a < 4x+15
Subtract 3a from both sides
ax+3a -3a< 4x+15-3a
ax < 4x+15-3a
ax-4x < 15-3a
x(a-4) < 15-3a
[tex]x < \frac{15-3a}{a-4}[/tex]
Like there is a variable a in the denominator, a-4 >0, then a>4.
Read more about inequalities here.
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