Weegy: Let's look at an example. If we are given the equation 3z + 5 +2z = 12 + 3z, we need to first combine like terms in each expression of this equation.
The two expressions in this equation are
3z + 5 +2z and 12 + 4z. [
3z + 5 +2z = 12 + 4z
There are three terms that contain the variable z: 3z, 2z, and 4z. We combine 3z, and 2z on the left side of the equation, then subtract 4z from both sides.
(3z +2z) + 5 = 12 + 4z
5z + 5 – 4z = 12 + 4z – 4z
z + 5 = 12
Notice we chose to subtract 4z from both sides rather than 5z. We chose to do this because consolidating in this manner left z positive. However, subtracting 5z from both sides would also be correct.
See how it works when we subtract 5z from both sides. 5z + 5 – 5z = 12 + 4z – 5z
5 = 12 – z
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Here's an example of an equation-solving procedure for a simple linear equation:
Step 1: Start with the equation you want to solve. Let's consider the equation: 2x + 5 = 11.
Step 2: Simplify the equation by performing any necessary operations. In this case, we can start by subtracting 5 from both sides of the equation:
2x + 5 - 5 = 11 - 5
This simplifies to:
2x = 6
Step 3: Isolate the variable. Since we want to solve for x, we need to isolate x on one side of the equation. In this case, we can divide both sides of the equation by 2:
(2x)/2 = 6/2
This simplifies to:
x = 3
Step 4: Check your solution. To verify if the solution is correct, substitute the value of x back into the original equation and see if it satisfies the equation. In our case, substituting x = 3 into the original equation:
2(3) + 5 = 11
6 + 5 = 11
11 = 11
Since the equation is true, we can conclude that x = 3 is indeed the solution to the equation.
This procedure can be applied to solve linear equations of varying complexity. For equations involving other types of functions, the procedure may differ, but the general idea is to simplify, isolate the variable, and check the solution.
Added 144 days ago|7/12/2023 10:51:40 AM
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