atic/chunks/29825-94580ffc5e6c1687.js","81779","static/chunks/81779-a1a04924c020dac8.js","28478","static/chunks/app/dn/qna/%5BquestionId%5D/page-6b55be924163beff.js"],"default"] 2c:T520,To solve the equation \((8x - 1)/2 + 3x - 4 = (1 + 2x)/3\), we will follow these steps: ### Step 1: Eliminate the fractions To eliminate the fractions, we can find a common denominator. The denominators are 2 and 3, so the least common multiple (LCM) is 6. We will multiply every term in the equation by 6: \[ 6 \left(\frac{8x - 1}{2}\right) + 6(3x - 4) = 6 \left(\frac{1 + 2x}{3}\right) \] ### Step 2: Simplify each term Now, we simplify each term: \[ 3(8x - 1) + 6(3x - 4) = 2(1 + 2x) \] Expanding each term gives us: \[ 24x - 3 + 18x - 24 = 2 + 4x \] ### Step 3: Combine like terms Now, we combine the like terms on the left side: \[ (24x + 18x) - 3 - 24 = 2 + 4x \] This simplifies to: \[ 42x - 27 = 2 + 4x \] ### Step 4: Move all terms involving \(x\) to one side Next, we will move all terms involving \(x\) to one side and constant terms to the other side. We do this by subtracting \(4x\) from both sides: \[ 42x - 4x - 27 = 2 \] This simplifies to: \[ 38x - 27 = 2 \] ### Step 5: Move constant terms to the right side Now, we add 27 to both sides: \[ 38x = 2 + 27 \] This simplifies to: \[ 38x = 29 \] ### Step 6: Solve for \(x\) Finally, we divide both sides by 38 to solve for \(x\): \[ x = \frac{29}{38} \] Thus, the solution to the equation is: \[ \boxed{\frac{29}{38}} \] ---2d:T5d5,To solve the equation \((8x - 1)/2 + 3x - 4 = (1 + 2x)/3\), we will follow these steps:
### Step 1: Eliminate the fractions
To eliminate the fractions, we can find a common denominator. The denominators are 2 and 3, so the least common multiple (LCM) is 6. We will multiply every term in the equation by 6:
\[
6 \left(\frac{8x - 1}{2}\right) + 6(3x - 4) = 6 \left(\frac{1 + 2x}{3}\right)
\]
### Step 2: Simplify each term
Now, we simplify each term:
\[
3(8x - 1) + 6(3x - 4) = 2(1 + 2x)
\]
Expandin

Solve for x: `(8x-1)/2+3x-4=(1+2x)/3`

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