Introduction
Greetings, readers! In this comprehensive guide, we’ll embark on a mathematical journey to solve the equation –3g–10=–6g+8. We’ll delve into various strategies and techniques to unravel the mysteries of this algebraic expression. So, grab a pen, paper, and a cup of coffee, and let’s get started!
Isolating the Variable: g
Step 1: Add 10 to Both Sides
To begin, let’s add 10 to both sides of the equation to isolate the term with the variable "g" on one side:
–3g–10 + 10 = –6g+8 + 10
–3g = –6g + 18
Step 2: Subtract –6g from Both Sides
Now, let’s subtract –6g from both sides to get "g" all by itself:
–3g – (–6g) = –6g + 18 – (–6g)
3g = 18
Solving for g
Step 3: Divide Both Sides by 3
Finally, to find the value of "g," we divide both sides by 3:
(3g) / 3 = 18 / 3
g = 6
Therefore, the solution to the equation –3g–10=–6g+8 is g = 6.
Applications of the Equation
The equation –3g–10=–6g+8 can have various practical applications, including:
Linear Equations in Physics
This equation can be used to solve problems related to motion, where "g" represents acceleration due to gravity.
Balancing Chemical Equations
In chemistry, this equation can be applied to balance chemical equations by adjusting the coefficients of reactants and products to ensure equal numbers of atoms on both sides.
Table Breakdown
| Variable | Value |
|---|---|
| g | 6 |
| Coefficient of g | -3 |
| Constant on the left side | -10 |
| Coefficient of g on the right side | -6 |
| Constant on the right side | 8 |
Conclusion
Congratulations, readers! You’ve successfully solved the equation –3g–10=–6g+8. Remember, practice is key when it comes to solving algebraic equations. If you’re interested in exploring more mathematical challenges, be sure to check out our other articles on solving equations, inequalities, and more. Until next time, stay curious and keep learning!
FAQ about “–3g–10=–6g+8”
How do I solve the equation “–3g–10=–6g+8”?
Combine like terms on both sides of the equation: -3g – 10 = -6g + 8 becomes -3g + 6g = 10 + 8, which simplifies to 3g = 18.
What is the value of g in the equation “–3g–10=–6g+8”?
Divide both sides of the equation by 3: 3g = 18 becomes g = 18/3, which simplifies to g = 6.
What is the first step in solving the equation “–3g–10=–6g+8”?
Add 6g to both sides of the equation: -3g – 10 + 6g = -6g + 8 + 6g.
What is the simplified form of the equation “–3g–10=–6g+8”?
-3g – 10 = -6g + 8 simplifies to 3g = 18.
What is the opposite of the equation “–3g–10=–6g+8”?
The opposite of the equation -3g – 10 = -6g + 8 is 3g + 10 = 6g – 8.
What is the equation of a line that is perpendicular to the line represented by the equation “–3g–10=–6g+8”?
The equation of a line perpendicular to the line represented by the equation -3g – 10 = -6g + 8 is 6g – y = c, where c is a constant.
What is the slope of the line represented by the equation “–3g–10=–6g+8”?
The slope of the line represented by the equation -3g – 10 = -6g + 8 is -3.
What is the y-intercept of the line represented by the equation “–3g–10=–6g+8”?
The y-intercept of the line represented by the equation -3g – 10 = -6g + 8 is -10.
What is the graph of the line represented by the equation “–3g–10=–6g+8”?
The graph of the line represented by the equation -3g – 10 = -6g + 8 is a straight line with a slope of -3 and a y-intercept of -10.
What is the solution set of the equation “–3g–10=–6g+8”?
The solution set of the equation -3g – 10 = -6g + 8 is {6}.
