solve each inequality:
1-2t>-5
and the answer is:
t<3
because you subtract one form both sides and get -2t>-6
and that's really positive and divide by 2 and that's where the three comes from
... but why does the > symbol change to < ?!
The reason the > symbol changes to < when solving an inequality is due to the operation of dividing or multiplying both sides by a negative number. Let's break down the steps of solving the inequality and explain why the symbol changes.
First, let's start with the original inequality:
1 - 2t > -5
To isolate t and find its value, we need to perform certain operations. The first step is to get rid of the constant term (-1) on the left side of the inequality. We can achieve this by subtracting 1 from both sides:
1 - 2t - 1 > -5 - 1
-2t > -6
Now, notice that there is a coefficient of -2 in front of t. To solve for t, we need to get rid of this coefficient. In order to do that, we divide both sides of the inequality by -2. However, it's important to note that when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality symbol changes. This is the key reason why the > symbol changes to <:
(-2t) / -2 < (-6) / -2
t < 3
So, the final solution is t < 3, indicating that any value of t less than 3 will satisfy the inequality 1 - 2t > -5.