Explain how to solve a multi-step equation.
To solve a multi-step equation, follow these steps:
1. Simplify each side of the equation as much as possible by combining like terms and using the distributive property if necessary.
2. Move all variable terms to one side of the equation by adding or subtracting the same value to both sides.
3. Move all constant terms to the other side of the equation by adding or subtracting the same value to both sides.
4. Use the inverse operations of multiplication and division to isolate the variable term. If the variable is multiplied or divided by a number, multiply or divide both sides of the equation by its reciprocal.
5. Continue simplifying both sides of the equation, combining like terms if possible.
6. Check the solution by substituting the value you obtained for the variable back into the original equation. If both sides are equal, then the solution is correct.
Here is an example to illustrate these steps:
Step 1: Simplify each side of the equation.
3(x + 2) + 5 = 4(2x - 1) + 3
3x + 6 + 5 = 8x - 4 + 3
3x + 11 = 8x - 1
Step 2: Move all variable terms to one side of the equation.
3x - 8x = -1 - 11
-5x = -12
Step 3: Move all constant terms to the other side of the equation.
-5x + 5x = -12 + 5x
0 = -12 + 5x
Step 4: Use the inverse operations to isolate the variable term.
-12 + 12 = 5x
0 = 5x
0/5 = x
x = 0
Step 5: Simplify both sides of the equation.
0 = 0
Step 6: Check the solution.
Substitute x = 0 back into the original equation.
3(0 + 2) + 5 = 4(2(0) - 1) + 3
3(2) + 5 = 4(-1) + 3
6 + 5 = -4 + 3
11 = -1
Since 11 is not equal to -1, the solution x = 0 is incorrect. Therefore, there is no solution to the equation.