When you're solving an equation with an = sign, you don't ever have to worry about the sign changing. But things are a little different if you're solving an inequality with <, >, <, or >, To solve the equation x - 2 = 5, you just add 2 to both sides. What happens if you change it to an inequality x - 2 < 5? Are the steps still the same?
Let's see by starting with an inequality that we know is true. We know that 4 is smaller than 6. We could write this as the inequality below.
What happens if we add the same number to both sides of the equation? Will it still be a true inequality?
If you add the same number to both sides of a true inequality, the new inequality will also be true. It basically just shifts everything over on the number line. If one side of the inequality was smaller than the other, it will still be smaller if you add the same number to both sides.
In other words, you can add the same number to both sides of an inequality and the sign will stay the same. To solve the equation x - 2 = 6, you just add 2 to both sides.
To solve the inequality x - 2 < 6, you follow the same exact steps and keep the sign the same.
Here's an example:
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