Question

Identify the solution of the inequality |9m| + 40 > 4 and the graph that represents it.

Answer 1

All real numbers.

Explanation:

The bars either side of an expression or a value are the absolute value symbol. "Absolute value" means how far a value is from zero. Therefore, the absolute value of a number is its positive numerical value.

Given inequality:

`|9m|+40 > 4`

Subtract 40 from both sides to isolate the absolute value on one side of the equation:

`\implies |9m|+40-40 > 4-40`

`\implies |9m| > -36`

As the absolute value of a number or expression is its positive numerical value:

`\implies |9m| \geq 0`

Therefore, as 9m is always greater than or equal to zero, it will always be greater than -36, regardless of the value of m.

Therefore, the solution of the given inequality is all real numbers.

Answer 2

• B) All real numbers

===========================

Given

• Inequality |9m| + 40 > 4

Solution

• |9m| + 40 > 4
• |9m| > - 40 + 4
• |9m| > - 36
• |m| > - 4

Since absolute value is never negative, this inequality is correct for any value of m.

Correct answer choice is B.