Ex 2:
-2x+7=22
-2x+7-7=22-7
-2x=15
-2x/(-2)=15/(-2) I do not have to switch the equality sign. Even if I did it would not look any different.
x=-7.5
Check:
-2x+7=22
-2(-7.5)+7=22 my solution is that x=-7.5 so I will just put that in to see if it works.
15+7=22
22=22
Yes. It does work. I have solved it correctly for sure. And I can write my solution as {x|x=-7.5} but usually with equations we just leave the solution as x=-7.5 because x is just one value and not a whole set. But you can use this set notation here too if you like.
To solve the equation -2x + 7 = 22, you followed the steps correctly. Here's a breakdown of how you arrived at the solution x = -7.5:
Step 1: Start with the original equation: -2x + 7 = 22.
Step 2: To isolate the variable on one side, subtract 7 from both sides of the equation: -2x + 7 - 7 = 22 - 7.
Step 3: Simplify the equation: -2x = 15.
Step 4: To solve for x, divide both sides of the equation by -2: -2x / -2 = 15 / -2.
Step 5: Simplify the equation: x = -7.5.
Step 6 (Optional): Check if the solution satisfies the original equation. Substitute x = -7.5 back into the equation to see if the left side equals the right side: -2(-7.5) + 7 = 22.
Step 7: Simplify the equation: 15 + 7 = 22.
Step 8: Evaluate the equation: 22 = 22.
The equation is true, which confirms that x = -7.5 is the correct solution.
The solution can be written as x = -7.5 or {x | x = -7.5}. In most cases, we prefer to use the single-value notation x = -7.5 since the variable represents one value, but set notation can also be used.