QuestionAugust 24, 2025

1. ESSENTIAL QUESTION How do you create equations with a variable on both sides and use them to solve problems?

1. ESSENTIAL QUESTION How do you create equations with a variable on both sides and use them to solve problems?
1. ESSENTIAL QUESTION How do you create equations with a variable on both sides and use them to solve problems?

Solution
4.7(303 votes)

Answer

The solution is x = 5. Explanation 1. Identify the Equation Start with an equation that has variables on both sides, e.g., 3x + 5 = 2x + 10. 2. Simplify Both Sides Combine like terms on each side if necessary. In this example, both sides are already simplified. 3. Move Variables to One Side Subtract 2x from both sides: 3x - 2x + 5 = 10. This simplifies to x + 5 = 10. 4. Isolate the Variable Subtract 5 from both sides: x + 5 - 5 = 10 - 5. This simplifies to x = 5. 5. Verify the Solution Substitute x = 5 back into the original equation to ensure both sides are equal: 3(5) + 5 = 2(5) + 10, which simplifies to 20 = 20.

Explanation

1. Identify the Equation<br /> Start with an equation that has variables on both sides, e.g., $3x + 5 = 2x + 10$.<br /><br />2. Simplify Both Sides<br /> Combine like terms on each side if necessary. In this example, both sides are already simplified.<br /><br />3. Move Variables to One Side<br /> Subtract $2x$ from both sides: $3x - 2x + 5 = 10$. This simplifies to $x + 5 = 10$.<br /><br />4. Isolate the Variable<br /> Subtract 5 from both sides: $x + 5 - 5 = 10 - 5$. This simplifies to $x = 5$.<br /><br />5. Verify the Solution<br /> Substitute $x = 5$ back into the original equation to ensure both sides are equal: $3(5) + 5 = 2(5) + 10$, which simplifies to $20 = 20$.
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