Two-Step Equations & Inequalities Word Problems

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What is a two-step equation?

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A two-step equation is an algebraic equation that requires two operations to solve for the variable. For example, in the equation 2x + 3 = 11, you would first subtract 3 and then divide by 2 to find x.

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What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. For example, x > 5 means x is greater than 5.

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How do you write an inequality for a situation where you need to save at least a certain amount of money?

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You can write an inequality by representing the total amount saved as a variable and setting it greater than or equal to the target amount. For example, if you have $30 and need at least $240, the inequality would be 30 + x ≥ 240.

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What does the variable 'x' typically represent in word problems involving money?

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In word problems involving money, 'x' often represents the unknown amount of money, such as the cost of an item or the number of items needed to reach a financial goal.

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How do you solve a two-step equation?

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To solve a two-step equation, perform the inverse operations in reverse order: first, isolate the variable by undoing the addition or subtraction, and then undo the multiplication or division.

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What is the first step in solving the equation 5x + 1.25 = 38.75?

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The first step is to subtract 1.25 from both sides of the equation to isolate the term with the variable: 5x = 38.75 - 1.25.

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What does it mean to 'reach a goal' in the context of inequalities?

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Reaching a goal in the context of inequalities means that the value represented by the variable must be equal to or exceed a specified target.

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How can you represent a situation where you have a fixed cost and a variable cost?

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You can represent this situation with an equation or inequality that combines the fixed cost with the variable cost multiplied by the number of items. For example, total cost = fixed cost + (variable cost per item * number of items).

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What is the significance of the '≥' symbol in an inequality?

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The '≥' symbol indicates that the value on the left is greater than or equal to the value on the right, meaning it can be equal to or exceed that value.

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How do you interpret the solution of an inequality?

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The solution of an inequality represents a range of values that satisfy the condition. For example, if x ≥ 10, any value of x that is 10 or greater is a solution.