Question

Is the given equation -5|5x-1|-10=-50 true or false?

Answer 1

The equation -5|5x-1|-10=-50 is true. When the absolute value is considered, there are two solutions for x: x = 1.8 and x = -1.4, both of which satisfy the original equation.

Step-by-step explanation:

Let's determine whether the equation -5|5x-1|-10=-50 is true or false. First, we add 10 to both sides of the equation to isolate the absolute value expression:

-5|5x-1| = -40

Next, we divide both sides by -5 to solve for the absolute value expression:

|5x-1| = 8

An absolute value equation can have two possible solutions, so let's consider both cases:

• 5x - 1 = 8
• 5x - 1 = -8

For the first case, when we solve for x, we get:

5x = 9
x = 1.8

For the second case, solving for x gives us:

5x = -7
x = -1.4

Both solutions make the original equation true, so the equation is true.