The solution to the linear equation 7x - 4 = 3x - 8 is found by eliminating and isolating terms, which results in x = -1. This value is checked against the original equation to ensure it is reasonable.
To find the solution to the equation 7x - 4 = 3x - 8, we need to isolate the variable x. First, we eliminate terms where possible by subtracting 3x from both sides: 7x - 3x - 4 = 3x - 3x - 8
This simplifies to: 4x - 4 = -8
Next, add 4 to both sides to further isolate the variable: 4x - 4 + 4 = -8 + 4
Which gives us: 4x = -4
Finally, divide both sides by 4 to find the value of x: x = -1
After calculating, we check the solution by substituting -1 back into the original equation to ensure that both sides equal.
7(-1) - 4 should equal 3(-1) - 8
-7 - 4 = -11 and -3 - 8 = -11, which confirms our solution is reasonable.