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(4) \( 34 x+1+x+x+3 x=8 \)

Ask by Brewer Morgan. in the United States
Feb 04,2025

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\( x = \frac{7}{39} \)

Solución

Sure, let's solve the equation step by step. **Given Equation:** \[ 34x + 1 + x + x + 3x = 8 \] **Step 1: Combine Like Terms** First, combine all the terms that have \( x \): \[ 34x + x + x + 3x = (34 + 1 + 1 + 3)x = 39x \] So, the equation simplifies to: \[ 39x + 1 = 8 \] **Step 2: Isolate the Term with \( x \)** Subtract 1 from both sides of the equation to move the constant term to the right side: \[ 39x + 1 - 1 = 8 - 1 \] \[ 39x = 7 \] **Step 3: Solve for \( x \)** Divide both sides by 39 to solve for \( x \): \[ x = \frac{7}{39} \] **Step 4: Simplify the Fraction (if possible)** Check if the numerator and the denominator have any common factors. - 7 is a prime number. - 39 factors into \( 3 \times 13 \). Since 7 doesn't divide evenly into 39, the fraction is already in its simplest form. **Final Answer:** \[ x = \frac{7}{39} \]

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The Deep Dive

To solve the equation \(34x + 1 + x + x + 3x = 8\), we start by simplifying the left side. Combine like terms: \(34x + 1 + x + x + 3x = 34x + 5x + 1 = 39x + 1\). Now the equation looks like this: \(39x + 1 = 8\). Next, we isolate \(x\) by subtracting 1 from both sides: \(39x = 8 - 1\), which simplifies to \(39x = 7\). Finally, divide both sides by 39 to solve for \(x\): \(x = \frac{7}{39}\). And there you have it, \(x\) is approximately \(0.179\) or \(7/39\) in fractional form! Feeling empowered by your algebra skills? You can practice similar equations by jumping into the world of linear equations for fun. It’s a fantastic way to better your math-savvy side while impressing your friends! Also, don't hesitate to revisit your algebra basics like combining like terms and isolating variables—these are super handy tools in your math toolbox, no matter how complex the equation may seem at first glance!

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