Question

Math

Posted 3 months ago

```
Solve for $a$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
$60 a+64 \geq 80 a-92$
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

Start with the given inequality: $60a + 64 \geq 80a - 92$

step 2

Subtract $60a$ from both sides to get: $64 \geq 20a - 92$

step 3

Add $92$ to both sides to isolate the term with $a$: $156 \geq 20a$

step 4

Divide both sides by $20$ to solve for $a$: $a \leq \frac{156}{20}$

step 5

Reduce the fraction to lowest terms: $a \leq \frac{39}{5}$

Answer

$a \leq \frac{39}{5}$

Key Concept

Solving inequalities

Explanation

To solve the inequality for $a$, we isolate $a$ on one side by performing inverse operations, such as subtracting and adding terms on both sides, and finally dividing by the coefficient of $a$. The inequality sign remains the same because we did not multiply or divide by a negative number.

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