Answer :
To solve the inequality [tex]\( |13x| > -5 \)[/tex], let's analyze the given absolute value expression step-by-step.
1. Understanding the Absolute Value Function: The absolute value function, written as [tex]\( |13x| \)[/tex], always gives a non-negative result. By definition:
[tex]\[ |13x| \geq 0 \][/tex]
This means that the smallest value [tex]\( |13x| \)[/tex] can take is [tex]\( 0 \)[/tex].
2. Comparing with [tex]\(-5\)[/tex]: Notice that [tex]\(-5\)[/tex] is a negative number. Since the absolute value of any real number is always non-negative, it is always greater than [tex]\(-5\)[/tex]:
[tex]\[ |13x| \geq 0 > -5 \][/tex]
3. Implications for [tex]\( x \)[/tex]: Since [tex]\( |13x| \)[/tex] is always non-negative and always greater than [tex]\(-5\)[/tex], this inequality is satisfied for all values of [tex]\( x \)[/tex]. No matter what [tex]\( x \)[/tex] you substitute into the expression [tex]\( 13x \)[/tex], the absolute value will always produce a value that is greater than [tex]\(-5\)[/tex].
Therefore, the correct answer is:
B. All values are solutions
1. Understanding the Absolute Value Function: The absolute value function, written as [tex]\( |13x| \)[/tex], always gives a non-negative result. By definition:
[tex]\[ |13x| \geq 0 \][/tex]
This means that the smallest value [tex]\( |13x| \)[/tex] can take is [tex]\( 0 \)[/tex].
2. Comparing with [tex]\(-5\)[/tex]: Notice that [tex]\(-5\)[/tex] is a negative number. Since the absolute value of any real number is always non-negative, it is always greater than [tex]\(-5\)[/tex]:
[tex]\[ |13x| \geq 0 > -5 \][/tex]
3. Implications for [tex]\( x \)[/tex]: Since [tex]\( |13x| \)[/tex] is always non-negative and always greater than [tex]\(-5\)[/tex], this inequality is satisfied for all values of [tex]\( x \)[/tex]. No matter what [tex]\( x \)[/tex] you substitute into the expression [tex]\( 13x \)[/tex], the absolute value will always produce a value that is greater than [tex]\(-5\)[/tex].
Therefore, the correct answer is:
B. All values are solutions
