Question

How would you figure this out?

Answer 1

I'm afraid that this is a weak attempt at your math teachers trying to teach you variables. Pretend that each shape is the letter x. Let's solve the first one together. 2x-1=5. To find what x=, you need to work backwards. Instead of subtracting one, add one. 5+1 is 6. Now you have 2x=6. Since x is being multiplied by 2, you need to divide 6 by 2. 6/2 is 3. x=3.
For the next one, we know that the triangle, or x, is 3. Again, let's make a different letter for the square. Let's make the square be y. Now your problem is 3 + y = 1. Once again, let's reverse our thinking to solve for what y=. 1-3 is -2. y=-2. See how that works? Now we need to Solve for the last one. The triangle, which we named x and is 3, and the square, which we named y and is -2, can be plugged into the final equation. 3-2(-2)=z. -2 * -2 is 4, and 3 + 4 is 7. Your final answer is 7.

Answer 2

$2\Delta-1=5\ \ \ |add\ 1\ to\ both\ sides\\2\Delta=6\ \ \ \ |divide\ both\ sides\ by\ 2\\\Delta=3\\----------------\\\Delta+\fbox{}=1\ \ \ \ |subtitute\ the\ value\ of\ \Delta\\3+\fbox{}=1\ \ \ \ |subtract\ 3\ from\ both\ sides\\\fbox{}=-2\\-----------------\\\Delta-2\fbox{}=*\ \ \ |subtitute\ values\ of\ \Delta\ and\ \fbox{}\\ *=3-2\cdot(-2)=3+4=7\\\\Answer{\boxed{\Delta=3;\ \fbox{}=-2;\ *=7}$