Remember: consecutive numbers are numbers that are back to back. For example, 1, 2, 3, and 4 are consecutive numbers while 1, 3, 5, and 6 are not.
Form your equation. Let x be your first number, x + 1 your second number, x + 2 your third, and x + 3 is your fourth. To further understand this, temporarily substitute 1 for x, and you will find that they are consecutive. (x) + (x + 1) + (x + 2) + (x + 3) = -26
Solve for x. (x) + (x + 1) + (x + 2) + (x + 3) = -26 Distributive Property x + x + 1 + x + 2 + x + 3 = -26 Combine like terms 4x + 1 + 2 + 3 = -26 Combine like terms 4x + 6 = -26 Subtract 6 from both sides 4x = -32 Divide by 4 to both sides x = -8 Isolated x
Substitute (-8) for x to find the numbers. 1st #: x = -8 2nd #: x + 1 = (-8) + 1 = -7 3rd #: x + 2 = (-8) + 2 = -6 4th #: x + 3 = (-8) + 3 = -5
The numbers are -8, -7, -6, and -5.
You can also check your work. (-8) + (-7) + (-6) + (-5) = -26 -26 = -26
If the absolute value expression is not equal to zero, the expression inside an absolute value can be either positive or negative. So, there can be at most two solutions. Looking at this graphically, an absolute value graph can intersect a horizontal line at most two times.
