Question

Explain why the solution of 5x – 3 > 14.5 or 5 x minus 3 greater than 14.5 or StartFraction 2 x plus 5 over 3 EndFraction less than 4. < 4 has a solution of all real numbers, with one exception.

Answer 1

Answer:

There is no point where x = 3.5

Step-by-step explanation:

Given the inequality

5x – 3 > 14.5

We are to find the range of all values of x

Add 3 to both sides of the equation;

5x - 3 + 3 > 14.5+ 3

5x > 17.5

x > 17.5/5

x > 3.5

Also for the inequality;

$\frac{2x+5}{3}$

Cross multiply;

$2x+5 < 3(4)\\2x + 5 < 12$

Subtract from both sides;

$2x + 5-5 < 12-5\\2x < 7\\x$

The solution to both inequalities are x > 3.5 and x < 3.5. Since there is no point where x = 3.5, hence the solution will have solution on all real numbers except at x = 3.5