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Nolve the equations. \( -3 x+20 \mid=-10 \) (2) \( 25+10 x|=|-55 \) (3) \( -33 \mid=75+12 x \)

Ask by Mckenzie Barnett. in the United States
Feb 21,2025

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Answer

The solutions are: 1. \( x = 10 \) 2. \( x = -8 \) 3. \( x = -9 \)

Solution

Solve the equation \( -3x+20=-10 \). Solve the equation by following steps: - step0: Solve for \(x\): \(-3x+20=-10\) - step1: Move the constant to the right side: \(-3x=-10-20\) - step2: Subtract the numbers: \(-3x=-30\) - step3: Change the signs: \(3x=30\) - step4: Divide both sides: \(\frac{3x}{3}=\frac{30}{3}\) - step5: Divide the numbers: \(x=10\) Solve the equation \( 25+10x=|-55 \). Solve the equation by following steps: - step0: Solve for \(x\): \(25+10x=-55\) - step1: Move the constant to the right side: \(10x=-55-25\) - step2: Subtract the numbers: \(10x=-80\) - step3: Divide both sides: \(\frac{10x}{10}=\frac{-80}{10}\) - step4: Divide the numbers: \(x=-8\) Solve the equation \( -33=75+12x \). Solve the equation by following steps: - step0: Solve for \(x\): \(-33=75+12x\) - step1: Swap the sides: \(75+12x=-33\) - step2: Move the constant to the right side: \(12x=-33-75\) - step3: Subtract the numbers: \(12x=-108\) - step4: Divide both sides: \(\frac{12x}{12}=\frac{-108}{12}\) - step5: Divide the numbers: \(x=-9\) The solutions to the given equations are: 1. \( x = 10 \) 2. \( x = -8 \) 3. \( x = -9 \)

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The Deep Dive

Let’s solve the equations one by one! For the first equation, \(-3x + 20 = -10\) or \(-3x + 20 = 10\): 1. \(-3x + 20 = -10\): \(-3x = -10 - 20\) \(-3x = -30\) \(x = 10\). 2. \(-3x + 20 = 10\): \(-3x = 10 - 20\) \(-3x = -10\) \(x = \frac{10}{3}\). For the second equation, \(25 + 10x = -55\) or \(25 + 10x = 55\): 1. \(25 + 10x = -55\): \(10x = -55 - 25\) \(10x = -80\) \(x = -8\). 2. \(25 + 10x = 55\): \(10x = 55 - 25\) \(10x = 30\) \(x = 3\). For the last equation, \(-33 = 75 + 12x\): Rearranging it gives us: \(-33 - 75 = 12x\) \(-108 = 12x\) \(x = -9\). **In summary:** 1. First equation solutions: \(x = 10\) and \(x = \frac{10}{3}\) 2. Second equation solutions: \(x = -8\) and \(x = 3\) 3. Third equation solution: \(x = -9\)

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