To express the statement "the sum of a number and 12.6 is more than -3.5" as an inequality, let's go through the steps carefully:
1. Identify the unknown number: Let's call this unknown number [tex]\( b \)[/tex].
2. Formulate the expression: According to the statement, "the sum of a number and 12.6" translates mathematically to [tex]\( b + 12.6 \)[/tex].
3. Translate the relational phrase "is more than": In mathematical language, "is more than" is represented by the inequality symbol [tex]\( > \)[/tex].
4. Combine the expression and the relation: Now, we combine the parts "the sum of a number and 12.6" with the relation "is more than -3.5". This gives us the inequality:
[tex]\[ b + 12.6 > -3.5 \][/tex]
Let's match this with the given options:
1. [tex]\( -3.5 + b \geq 12.6 \)[/tex] - This option is incorrect because it incorrectly places the constants and variables on opposite sides of the inequality and uses the wrong inequality symbol.
2. [tex]\( -3.5 + b < 12.6 \)[/tex] - This option is incorrect because it represents an inequality that contradicts the original statement.
3. [tex]\( b + 12.6 > -3.5 \)[/tex] - This option is correct as it accurately translates the given verbal statement into a mathematical inequality.
4. [tex]\( b + 12.6 \leq -3.5 \)[/tex] - This option is incorrect because it uses the incorrect inequality symbol and doesn't align with the statement "is more than".
Therefore, the inequality that correctly represents "the sum of a number and 12.6 is more than -3.5" is:
[tex]\[ b + 12.6 > -3.5 \][/tex]
So, the correct answer is:
[tex]\[ \boxed{b + 12.6 > -3.5} \][/tex]
