Problem Solving with Multi-Step Equations Quick Check

Answer 1

To solve multi-step equations, follow these steps:

1. Simplify both sides of the equation by combining like terms if possible.

2. Isolate the variable term by undoing addition or subtraction first. If the variable term is being added, subtract it from both sides. If the variable term is being subtracted, add it to both sides.

3. Undo multiplication or division next. If the variable term is being multiplied, divide both sides by that number. If the variable term is being divided, multiply both sides by that number.

4. Check your answer by substituting it back into the original equation. If both sides of the equation are equal, then your solution is correct.

Example:

Solve the equation 3(2x + 4) - 6 = 12.

Step 1: Simplify both sides.
6x + 12 - 6 = 12
6x + 6 = 12

Step 2: Isolate the variable term.
6x = 12 - 6
6x = 6

Step 3: Undo multiplication.
x = 6/6
x = 1

Step 4: Check the solution.
3(2(1) + 4) - 6 = 12
3(2 + 4) - 6 = 12
3(6) - 6 = 12
18 - 6 = 12
12 = 12

The solution, x = 1, checks out.