Solve the equation in part (b). Explain how you solved the equation and what the solution represents. Can you start with a different first step?
As mentioned in part (b), the equation to be solved is:
4x + 3 = 7x - 1
To solve this equation, we need to isolate the variable x on one side of the equation.
Starting with the original equation, we can first subtract 4x from both sides so that the x terms are on one side and the constant terms are on the other side:
4x + 3 - 4x = 7x - 1 - 4x
Simplifying on both sides, we get:
3 = 3x - 1
To further isolate the variable, we can add 1 to both sides of the equation to get:
3 + 1 = 3x - 1 + 1
Simplifying further, we get:
4 = 3x
Finally, we need to solve for x by dividing both sides of the equation by 3:
4/3 = (3x)/3
Simplifying, we have:
4/3 = x
So the solution to the equation is x = 4/3.
This solution represents the value of x which satisfies the equation. Substituting x = 4/3 back into the original equation, we get:
4(4/3) + 3 = 7(4/3) - 1
Simplifying further, we have:
16/3 + 3 = 28/3 - 1
Multiplying through by 3 to clear the fraction, we get:
16 + 9 = 28 - 3
25 = 25
As we can see, both sides of the equation are equal, confirming that x = 4/3 is indeed the solution to the equation.