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1. \( 2 x+7=15 \) 2. \( 3 y-5=10 \) 3. 4. 4 \( 6 b-1=-11=9 \) 5. \( 5 c+8=3 \)

Ask by Alexander Gonzalez. in the United States
Jan 23,2025

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Answer

The solutions are: 1. \( x = 4 \) 2. \( y = 5 \) 3. \( b = -\frac{5}{3} \) or \( b = -1.6 \) 4. \( c = -1 \)

Solution

Solve the equation \( 2x+7=15 \). Solve the equation by following steps: - step0: Solve for \(x\): \(2x+7=15\) - step1: Move the constant to the right side: \(2x=15-7\) - step2: Subtract the numbers: \(2x=8\) - step3: Divide both sides: \(\frac{2x}{2}=\frac{8}{2}\) - step4: Divide the numbers: \(x=4\) Solve the equation \( 3y-5=10 \). Solve the equation by following steps: - step0: Solve for \(y\): \(3y-5=10\) - step1: Move the constant to the right side: \(3y=10+5\) - step2: Add the numbers: \(3y=15\) - step3: Divide both sides: \(\frac{3y}{3}=\frac{15}{3}\) - step4: Divide the numbers: \(y=5\) Solve the equation \( 6b-1=-11 \). Solve the equation by following steps: - step0: Solve for \(b\): \(6b-1=-11\) - step1: Move the constant to the right side: \(6b=-11+1\) - step2: Add the numbers: \(6b=-10\) - step3: Divide both sides: \(\frac{6b}{6}=\frac{-10}{6}\) - step4: Divide the numbers: \(b=-\frac{5}{3}\) Solve the equation \( 5c+8=3 \). Solve the equation by following steps: - step0: Solve for \(c\): \(5c+8=3\) - step1: Move the constant to the right side: \(5c=3-8\) - step2: Subtract the numbers: \(5c=-5\) - step3: Divide both sides: \(\frac{5c}{5}=\frac{-5}{5}\) - step4: Divide the numbers: \(c=-1\) The solutions to the given equations are: 1. \(2x+7=15\) has the solution \(x=4\). 2. \(3y-5=10\) has the solution \(y=5\). 3. \(6b-1=-11\) has the solution \(b=-\frac{5}{3}\) or \(b=-1.6\). 4. \(5c+8=3\) has the solution \(c=-1\).

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Bonus Knowledge

Did you know that algebra dates back to ancient civilizations? The term "algebra" comes from the Arabic word "al-jabr," which means "the reunion of broken parts." This branch of mathematics developed in the 9th century through the works of mathematicians like Al-Khwarizmi, making it an essential part of the mathematical world today! When solving equations like those you've listed, it's easy to make small errors. A common mistake is forgetting to invert the sign when moving a term from one side of the equation to the other. For instance, when isolating \( x \) in \( 2x + 7 = 15 \), subtract 7, and you'll get \( 2x = 8 \). Always double-check your operations to avoid those little slip-ups!

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