Question

What values make the equations true? Use properties of addition to rewrite the expressions.

Options:
Option 1: 5x + 3 = 12
Option 2: 2y - 7 = 1
Option 3: 4z + 6 = 18
Option 4: 8a - 10 = 22

Answer 1

By using subtraction and division, we have found the values for variables in the given equations: x = 1.8 for 5x + 3 = 12, y = 4 for 2y - 7 = 1, z = 3 for 4z + 6 = 18, and a = 4 for 8a - 10 = 22.

Step-by-step explanation:

To find the values that make the given equations true, we will isolate the variable on one side of the equation using properties of addition and subtraction and operations like addition, subtraction, multiplication, and division. Here's how we solve each option:

1. Option 1: 5x + 3 = 12. To solve for x, subtract 3 from both sides of the equation to get 5x = 9, and then divide both sides by 5 to find x = 9/5 or x = 1.8.
2. Option 2: 2y - 7 = 1. Add 7 to both sides of the equation to get 2y = 8, and then divide both sides by 2 to find y = 4.
3. Option 3: 4z + 6 = 18. Subtract 6 from both sides to get 4z = 12, and then divide by 4 to find z = 3.
4. Option 4: 8a - 10 = 22. Add 10 to both sides to get 8a = 32, and then divide by 8 to find a = 4.

Using properties of addition and subtraction, we have successfully solved the equations and found the values for x, y, z, and a that make these equations true.

As a reminder, when subtracting, we change the sign of the subtracted number and follow the rules of addition: subtract the smaller number from the larger number and keep the sign of the larger number, as we did in Option 2 and Option 4.

To check our work, it's important to substitute the found values back into the original equations to make sure they hold true and that our answers are reasonable.