Questions: Solve the following equation. Be sure to check your proposed solution by substituting it for the variable in the given equation. 6x-4=3x-70

Solution Steps

To solve the equation \(6x - 4 = 3x - 70\), we need to isolate the variable \(x\). First, we'll move all terms involving \(x\) to one side of the equation and constant terms to the other side. Then, we'll solve for \(x\) by performing basic arithmetic operations. Finally, we'll substitute the solution back into the original equation to verify its correctness.

We start with the equation: \[ 6x - 4 = 3x - 70 \]

To isolate \(x\), we first move all terms involving \(x\) to one side and constant terms to the other side. We subtract \(3x\) from both sides: \[ 6x - 3x - 4 = -70 \] This simplifies to: \[ 3x - 4 = -70 \]

Next, we add \(4\) to both sides: \[ 3x = -70 + 4 \] This simplifies to: \[ 3x = -66 \]

Now, we divide both sides by \(3\): \[ x = \frac{-66}{3} \] This simplifies to: \[ x = -22 \]

To verify, we substitute \(x = -22\) back into the original equation: \[ 6(-22) - 4 = 3(-22) - 70 \] Calculating both sides: \[ -132 - 4 = -66 - 70 \] This simplifies to: \[ -136 = -136 \] Since both sides are equal, our solution is verified.

Final Answer