Solve for x: x=2 · GPTStore

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Solve this: –(–8–3x)=–2(1–x)+6x

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To solve the equation (-(-8 - 3x) = -2(1 - x) + 6x), let's simplify each side step by step.

First, simplify the left side of the equation: [-(-8 - 3x)] This double negative can be simplified to: [8 + 3x]

Now, simplify the right side of the equation: [-2(1 - x) + 6x] Distribute the -2 inside the parentheses: [-2 + 2x + 6x] Combine like terms: [2x + 6x - 2] [8x - 2]

Now the equation is: [8 + 3x = 8x - 2]

Next, we'll solve for x. To do that, let's get all the x terms on one side and the constants on the other side. Subtract 3x from both sides: [8 = 5x - 2]

Now, isolate x by moving the constant to the other side. Add 2 to both sides: [8 + 2 = 5x] [10 = 5x]

Finally, divide both sides by 5 to solve for x: [x = \frac{10}{5}] [x = 2]

So, the solution to the equation is (x = 2).

To solve the equation \(-(-8 - 3x) = -2(1 - x) + 6x\), let's simplify each side step by step. First, simplify the left side of the equation: \[-(-8 - 3x)\] This double negative can be simplified to: \[8 + 3x\] Now, simplify the right side of the equation: \[-2(1 - x) + 6x\] Distribute the -2 inside the parentheses: \[-2 + 2x + 6x\] Combine like terms: \[2x + 6x - 2\] \[8x - 2\] Now the equation is: \[8 + 3x = 8x - 2\] Next, we'll solve for x. To do that, let's get all the x terms on one side and the constants on the other side. Subtract 3x from both sides: \[8 = 5x - 2\] Now, isolate x by moving the constant to the other side. Add 2 to both sides: \[8 + 2 = 5x\] \[10 = 5x\] Finally, divide both sides by 5 to solve for x: \[x = \frac{10}{5}\] \[x = 2\] So, the solution to the equation is \(x = 2\).