Question

|2x+5|=|8x+2|

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Answer 1

Answer: x= 1/2

Subtract 5 from both sides, simplify it then subtract the numbers, Subtract 8x from both sides. Divide -6 for both sides then simplify and you get 1/2

Answer 2

To solve the equation |2x + 5| = |8x + 2|, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: When the expression inside the absolute value is positive:

We can remove the absolute value symbols without changing the equation: 2x + 5 = 8x + 2

Case 2: When the expression inside the absolute value is negative:

We need to negate the expression inside the absolute value and remove the absolute value symbols: -(2x + 5) = 8x + 2

Now, let’s solve each case separately:

Case 1:

Subtracting 2x from both sides of the equation, we get: 5 = 6x + 2

Subtracting 2 from both sides of the equation, we get: 3 = 6x

Dividing both sides of the equation by 6, we get: x = \frac{1}{2}

Case 2:

Distributing the negative sign, we get: -2x - 5 = 8x + 2

Adding 2x to both sides of the equation, we get: -5 = 10x + 2

Subtracting 2 from both sides of the equation, we get: -7 = 10x

Dividing both sides of the equation by 10, we get: x = -\frac{7}{10}

Therefore, the solutions to the equation |2x + 5| = |8x + 2| are x = \frac{1}{2} and x = -\frac{7}{10}.