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Answer :
Sure! Let's translate the statement "negative 12 times [tex]$f$[/tex] plus 18 is at least 89" into a mathematical inequality.
1. Identify the components of the statement:
- "Negative 12 times [tex]$f$[/tex]" translates to [tex]\(-12f\)[/tex].
- "Plus 18" indicates that we add 18 to [tex]\(-12f\)[/tex], which gives us [tex]\(-12f + 18\)[/tex].
- "Is at least 89" means that the expression [tex]\(-12f + 18\)[/tex] must be greater than or equal to 89.
2. Combine these components into an inequality:
- The inequality that correctly represents the statement is [tex]\(-12f + 18 \geq 89\)[/tex].
3. Verify with the given options:
- Option 1: [tex]\(-12f + 18 \leq 28\)[/tex] does not match because it uses "[tex]\(\leq\)[/tex]" and relates to 28, not 89.
- Option 2: [tex]\(-12f + 18 \geq 89\)[/tex] matches our derived inequality perfectly.
- Option 3: [tex]\(-12(f + 18) \leq 89\)[/tex] involves incorrect grouping and uses "[tex]\(\leq\)[/tex]".
- Option 4: [tex]\(-12(f + 18) \geq 89\)[/tex] involves incorrect grouping, though it uses "[tex]\(\geq\)[/tex]".
Thus, the correct inequality is [tex]\(-12f + 18 \geq 89\)[/tex], which corresponds to Option 2.
1. Identify the components of the statement:
- "Negative 12 times [tex]$f$[/tex]" translates to [tex]\(-12f\)[/tex].
- "Plus 18" indicates that we add 18 to [tex]\(-12f\)[/tex], which gives us [tex]\(-12f + 18\)[/tex].
- "Is at least 89" means that the expression [tex]\(-12f + 18\)[/tex] must be greater than or equal to 89.
2. Combine these components into an inequality:
- The inequality that correctly represents the statement is [tex]\(-12f + 18 \geq 89\)[/tex].
3. Verify with the given options:
- Option 1: [tex]\(-12f + 18 \leq 28\)[/tex] does not match because it uses "[tex]\(\leq\)[/tex]" and relates to 28, not 89.
- Option 2: [tex]\(-12f + 18 \geq 89\)[/tex] matches our derived inequality perfectly.
- Option 3: [tex]\(-12(f + 18) \leq 89\)[/tex] involves incorrect grouping and uses "[tex]\(\leq\)[/tex]".
- Option 4: [tex]\(-12(f + 18) \geq 89\)[/tex] involves incorrect grouping, though it uses "[tex]\(\geq\)[/tex]".
Thus, the correct inequality is [tex]\(-12f + 18 \geq 89\)[/tex], which corresponds to Option 2.
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