Final answer:
The question asks to solve four linear equations utilizing properties of equality, resulting in the solutions t=2, x=10, x=3, and y=29 respectively.
Step-by-step explanation:
The question involves solving linear equations in one variable using properties of equality. The first equation, 2t - 4 = 0, can be solved by adding 4 to both sides to obtain 2t = 4, and then dividing both sides by 2, yielding t = 2. For the second equation, 4x = 20 + 2x, we subtract 2x from both sides to get 2x = 20, and then divide by 2, resulting in x = 10. The third equation, 6x - 5 = 2x + 7, requires us to subtract 2x from both sides, which gives us 4x - 5 = 7, and then add 5 to both sides, thus 4x = 12, and finally divide by 4, arriving at x = 3.
Lastly, for the equation 3(y - 24) = 15, we first distribute the 3 to get 3y - 72 = 15, then add 72 to both sides, which gives us 3y = 87, and when we divide both sides by 3, we end up with y = 29. Each step methodically applies properties of equality such as addition property, subtraction property, multiplication property, and division property, to isolate the variable and solve for its value.