how do you solve -3 + 5 +6g =11 – 3g?
The correct answer and explanation is:
Let’s solve the equation: −3+5+6g=11−3g-3 + 5 + 6g = 11 – 3g
Step 1: Simplify both sides
On the left side, combine the constant terms −3+5-3 + 5: 2+6g=11−3g2 + 6g = 11 – 3g
Step 2: Get all terms containing gg on one side
Add 3g3g to both sides to move all gg-terms to the left: 2+6g+3g=11−3g+3g2 + 6g + 3g = 11 – 3g + 3g
This simplifies to: 2+9g=112 + 9g = 11
Step 3: Isolate the term with gg
Subtract 2 from both sides to move constants to the right: 9g=11−29g = 11 – 2
Simplify the right side: 9g=99g = 9
Step 4: Solve for gg
Divide both sides by 9 to isolate gg: g=99=1g = \frac{9}{9} = 1
Final answer: g=1g = 1
Explanation
The goal in solving linear equations with variables on both sides is to isolate the variable on one side and constants on the other. First, simplify each side by combining like terms to make the equation easier to work with. This reduces mistakes and clarifies what terms remain. Then, use inverse operations such as addition or subtraction to move variable terms to one side of the equation and constants to the other.
After grouping terms, simplify again. The next step is to isolate the variable by undoing multiplication or division. In this example, the variable gg was multiplied by 9 after combining like terms, so dividing both sides by 9 isolates gg.
This method maintains equality by performing the same operation on both sides of the equation. Each step transforms the equation without changing its solutions. Finally, the value found for gg can be substituted back into the original equation to verify correctness.
This structured approach ensures that the solution is accurate and the steps can be easily followed and checked.