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Math Word Problems - Equations

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    Study Guide Math Word Problems – Equations 1. Keywords Indicating Equality One of the hardest parts of solving word problems is writing the correct equation . Once the equation is written correctly, solving it is usually much easier. To write the correct equation, you must recognize keywords that indicate equality . These words tell you where to place the equal sign (=) . 1.1 Equality Keywords The following words and phrases translate directly to the equal sign (=) : • IS • IS EQUAL TO • EQUALS • YIELDS • RESULTS IN • THE RESULT IS • IS THE SAME AS These keywords use the direct translation strategy . That means: • You do not change the order • You place = exactly where the equality word appears Example 1: Writing an Equation with Multiple Keywords Twice the difference between a number and five is equal to negative fourteen

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    Study Guide Step - by - Step Translation 1. Group adjacent keywords Place parentheses around the expression that comes after Twice and before IS : Twice (the difference between a number and five) is equal to negative fourteen 2. Identify the subtraction phrase The leading keyword DIFFERENCE BETWEEN tells you subtraction: o a number − five 3. Translate each part o Twice → multiply by 2 o Difference between a number and five → ( x − 5 ) o Is equal to → ( = ) o Negative fourteen → ( - 14 ) Final Equation 2(x - 5) = - 14 Important note: The word TO in IS EQUAL TO is not a turnaround word. Equality keywords always use direct translation . Example 2: When “IS” Does Not Mean Equals

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    Study Guide Key Idea Not every IS means “equals.” • The first IS introduces an operation (subtracted) • The second IS indicates equality Step - by - Step Translation • “a number subtracted from twelve” → ( 12 - x ) • “the result is five” → ( = 5 ) Final Equation 12 - x = 5 Tip: If IS comes right before a number, it usually means equals . If IS comes before an operation word, it does not mean equals. Example 3: Equality with a Leading Keyword The product of eight and a number yields twenty - four Step - by - Step Translation 1. Translate the first expression o Product of eight and a number → ( 8x ) 2. Translate the equality keyword o Yields → ( = ) 3. Translate the second expression o Twenty - four → ( 24 )

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