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Michael wants to purchase a precision balance of 340 dollars.
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He already has 113 dollars saved and can save 28 dollars per week.
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Write an inequality that can be used to determine the number of weeks left for Michael to save at least 340 dollars.
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We will let π₯ equal the number of weeks.
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As Michael can save 28 dollars per week, the amount of money that he can save over a longer period of time will be 28 multiplied by π₯, which we can write as 28π₯.
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Michael has already saved 113 dollars, so we can add this to our 28π₯.
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As Michael needs to save at least 340 dollars, we are going to use the greater than or equal to or more than or equal to sign.
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And the amount of money he wants to save is 340 dollars.
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Therefore our equation, our inequality, is 28π₯ plus 113 is more than or equal to 340.
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Whilst weβre not asked to work out the value of π₯ in this particular question, Iβll go through that process for you now.
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To solve an inequality, we treat it in exactly the same way as an equation and use the balancing method.
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Our first step would be to subtract 113 from both sides of the equation.
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This would leave us with 28π₯ is more than or equal to 227.
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Dividing both sides of the equation by 28 leaves us with π₯ is more than or equal to 8.107.
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As the number of weeks can only be a whole number or an integer value, we know that the number of weeks that Michael would need to save for is nine weeks.