Final answer:
To solve for x in the four given linear equations using a=2 and b=3, we would rearrange each equation to isolate x. The process involves basic algebraic manipulations such as adding, subtracting, multiplying, or dividing both sides of the equation as necessary.
Step-by-step explanation:
To solve the equations provided for x, we need to manipulate each equation such that x is isolated on one side of the equation. Below I will demonstrate how to solve each given linear equation using the specified values of a = 2 and b = 3.
For the first equation, represented by y = mx + b, where m and b are constants, we would rearrange the equation to solve for x. If we were given specific values for y and m, we could use the steps of subtracting b from both sides of the equation and then dividing by m to find x.
In the second exercise, with the equation of y = x + 4, we simply subtract 4 from both sides to isolate x: x = y - 4.
The third exercise presents the equation y = 100x + 2,000. To solve for x, you would subtract 2,000 from both sides and then divide by 100: x = (y - 2000) / 100.
Lastly, the fourth equation, y = 3,000x + 500, is solved for x by subtracting 500 from both sides and then dividing by 3,000: x = (y - 500) / 3000.
Remember that solving for x typically involves isolating the variable x on one side of the equation while moving everything else to the other side, using addition, subtraction, multiplication, and division operations as appropriate.