Solving for a variable like ‘g’ in an equation is a fundamental skill in algebra. Let’s walk through the process step by step with an example.
Example Equation
Suppose we have the equation:
$3g + 5 = 20$
Step-by-Step Solution
- Isolate the Term with g
First, we want to isolate the term that contains ‘g’. To do this, we need to get rid of the constant on the same side as ‘g’. In this case, we need to subtract 5 from both sides of the equation:
$3g + 5 – 5 = 20 – 5$
This simplifies to:
$3g = 15$
- Solve for g
Next, we need to isolate ‘g’ by itself. Since ‘g’ is currently multiplied by 3, we need to divide both sides by 3:
$frac{3g}{3} = frac{15}{3}$
This simplifies to:
$g = 5$
Verification
To ensure our solution is correct, we can substitute ‘g’ back into the original equation:
$3(5) + 5 = 20$
This simplifies to:
$15 + 5 = 20$
$20 = 20$
Since both sides of the equation are equal, our solution is verified.
More Complex Example
Let’s consider a more complex equation:
$4g – 2g + 7 = 3g + 10$
- Simplify Both Sides
First, combine like terms:
$2g + 7 = 3g + 10$
- Isolate the Term with g
Next, we want to isolate the term with ‘g’ on one side. Subtract 3g from both sides:
$2g – 3g + 7 = 10$
This simplifies to:
$-g + 7 = 10$
- Isolate g
Subtract 7 from both sides:
$-g + 7 – 7 = 10 – 7$
This simplifies to:
$-g = 3$
- Solve for g
Multiply both sides by -1 to solve for ‘g’:
$g = -3$
Verification
Substitute ‘g’ back into the original equation:
$4(-3) – 2(-3) + 7 = 3(-3) + 10$
This simplifies to:
$-12 + 6 + 7 = -9 + 10$
$1 = 1$
Since both sides of the equation are equal, our solution is verified.
Conclusion
Solving for ‘g’ involves isolating the variable by performing inverse operations, simplifying the equation step by step, and verifying the solution. Mastering these steps will help you tackle any algebraic equation with confidence.