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Solve the following equation for \( x \). Express your answer in the simplest form. \[ 8(3 x+1)=8(-3 x-1) \] Answer Attempt 1 out of 2 The equation has Submit Answer

Ask by Wang Williams. in the United States
Feb 21,2025

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Answer

\( x = -\frac{1}{3} \)

Solution

Solve the equation \( 8(3x+1)=8(-3x-1) \). Solve the equation by following steps: - step0: Solve for \(x\): \(8\left(3x+1\right)=8\left(-3x-1\right)\) - step1: Calculate: \(24x+8=8\left(-3x-1\right)\) - step2: Calculate: \(24x+8=-24x-8\) - step3: Move the expression to the left side: \(24x+8-\left(-24x-8\right)=0\) - step4: Calculate: \(48x+16=0\) - step5: Move the constant to the right side: \(48x=0-16\) - step6: Remove 0: \(48x=-16\) - step7: Divide both sides: \(\frac{48x}{48}=\frac{-16}{48}\) - step8: Divide the numbers: \(x=-\frac{1}{3}\) The solution to the equation \(8(3x+1)=8(-3x-1)\) is \(x=-\frac{1}{3}\) or \(x=-0.\dot{3}\).

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Beyond the Answer

To solve the equation \( 8(3x + 1) = 8(-3x - 1) \), first, we can divide both sides by 8: \[ 3x + 1 = -3x - 1 \] Next, we can add \( 3x \) to both sides: \[ 3x + 3x + 1 = -1 \] This simplifies to: \[ 6x + 1 = -1 \] Now, subtract 1 from both sides: \[ 6x = -2 \] Finally, divide both sides by 6: \[ x = -\frac{1}{3} \] So, the solution in its simplest form is \( x = -\frac{1}{3} \).

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