1558+60x≥ 2158
The correct answer and explanation is:
To solve the inequality 1558+60x≥21581558 + 60x \geq 2158, follow these steps:
- Isolate the variable term (60x):
Start by subtracting 1558 from both sides of the inequality: 1558+60x−1558≥2158−15581558 + 60x – 1558 \geq 2158 – 1558 This simplifies to: 60x≥60060x \geq 600 - Solve for x:
Now divide both sides of the inequality by 60: 60×60≥60060\frac{60x}{60} \geq \frac{600}{60} Simplifying gives: x≥10x \geq 10
Thus, the solution is x≥10x \geq 10. This means that xx must be equal to or greater than 10 to satisfy the inequality.
Explanation:
In the given inequality, we first isolate the term containing the variable xx by moving the constant (1558) to the other side of the inequality. This is done by subtracting 1558 from both sides. Once the variable term is isolated, we solve for xx by dividing both sides by 60, the coefficient of xx.
The inequality tells us that xx can take any value greater than or equal to 10. This means the solution set includes all values of xx starting from 10 and extending infinitely. In interval notation, the solution is written as [10,∞)[10, \infty).
This approach can be applied to similar inequalities involving multiplication and addition of constants to a variable term. The key steps are isolating the variable and then solving for it using basic algebraic operations.