which number is a the solution of the equation [5x-2] = 8?
a.}6/5
b.}1/2
c.}negative 6/5
d.}negative 1
Is this [5x - 2] supposed to represent absolute value of 5x - 2 ? If so, set up two equations:
5x - 2 = 8
and
5x - 2 = -8
Solve each and see if one of the solutions is included in your selection of answers.
I hope this will help.
To find the solution to the equation [5x - 2] = 8, you need to consider both the positive and negative values of the expression inside the absolute value brackets. This is because the absolute value function represents the distance from zero, so it can be positive or negative.
First, let's consider the positive case: 5x - 2 = 8. Add 2 to both sides of the equation: 5x = 10. Divide both sides by 5: x = 2.
Now, let's consider the negative case: 5x - 2 = -8. Add 2 to both sides of the equation: 5x = -6. Divide both sides by 5: x = -6/5 = -1.2.
Now, check if either of the solutions, x = 2 or x = -1.2, is included in the given options: a) 6/5, b) 1/2, c) -6/5, d) -1.
Only option d) -1 matches one of the solutions we found, so the correct answer is d) -1.
Remember, when faced with an absolute value equation, always consider both the positive and negative cases and solve separately.