Question

The inequality x + 5 < x + 4 has no solutions. Explain why

Answer 1

Subtract x from both sides and we go from

x+5 < x+4

to

5 < 4

The x terms cancel out. What we're left with is a false statement. The number 5 is never smaller than 4. Therefore, the original inequality is always false as well. No matter what number you replace x with, you'll never get a true statement. Let's try x = 10

x+5 < x+4

10+5 < 10+4

15 < 14

which is false. I'll let you try other x values. So this is why the inequality has no solutions. A solution is something we replace x with to make the inequality a true statement.

Answer 2

An inequality may or may not have solutions.

The inequality x + 5 < x + 4 does not have a solution because it is not true

The inequality is given as:

$x + 5 < x + 4$

Subtract x from both sides of the inequality

$x -x + 5 < x -x + 4$

Evaluate like terms

$5 < 4$

The above inequality means;

5 is less than 4

This is not true because 5 is not less than 4; instead it is greater than 4

Hence, the inequality x + 5 < x + 4 does not have a solution because it is not true

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