Pay attention to the operations indicated in the equation and what conditions they impose over the possible values of x.
Negative, see solution.
Practice makes perfect
We are given an equation and asked to tell if the value of x will be negative or positive without solving the equation.
-3x+5=44
First of all, notice that the quantity at the right-hand side is positive. This means that the quantity on the left-hand side should be positive as well.
-3x+5 > 0
From here, we can consider the two cases — when x is positive versus when x is negative.
Positive Value of x
For the quantity on the left-hand side to be positive with a positive x, the product of -3 and x must result in a number less than 5.
- 3x + 5 > 0 ⇒ 3 x < 5
This possibility only allows for values of x such that -3x+5 would yield a small positive value. The left-hand side would always equal a number much less than 44. Hence, the equality -3x+5=44 would never hold.
Negative Value of x
On the other hand, let's assume x is a negative number. Then we have the following condition.
x<0 ⇒ -3x>0
This is true because a negative multiplied by a negative is always a positive number. It follows that the left-hand side of the equation would be greater than 0 for any negative value of x.
-3x+5>0
One such value would satisfy the given equation, -3x+5=44. Thus, x must be negative.
