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

When solving the first inequality, you get x > 3.5. When solving the second inequality, you get x < 3.5. The solution of an "or” compound in equality is everything in both solution sets, so the solution set is all of the numbers less than 3.5 and greater than 3.5. Since neither of the inequalities includes 3.5, the compound inequality has a solution of all real numbers except 3.5.

Explanation:

Answer 2

There is no point where x = 3.5

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;

`(2x+5)/(3) <4\\`

Cross multiply;

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

Subtract from both sides;

`2x + 5-5 < 12-5\\2x < 7\\x<7/2\\x<3.5`

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