What Is The Value Of $x$ In The Equation $0.7x - 1.4 = -3.5$?A. − 7 -7 − 7 B. − 3 -3 − 3 C. 3 3 3 D. 7 7 7
Understanding the Equation
To find the value of $x$ in the equation $0.7x - 1.4 = -3.5$, we need to isolate the variable $x$. This involves adding or subtracting the same value to both sides of the equation to maintain the equality. The equation is a linear equation, and we can solve it using basic algebraic operations.
Isolating the Variable
The first step in solving the equation is to isolate the term containing the variable $x$. We can do this by adding $1.4$ to both sides of the equation. This will eliminate the constant term on the left side of the equation.
Simplifying the Equation
After adding $1.4$ to both sides of the equation, we get:
Now, we can simplify the right side of the equation by performing the addition.
Solving for $x$
To solve for $x$, we need to isolate the variable by dividing both sides of the equation by $0.7$. This will give us the value of $x$.
Calculating the Value of $x$
After dividing both sides of the equation by $0.7$, we get:
Now, we can calculate the value of $x$ by performing the division.
Conclusion
In conclusion, the value of $x$ in the equation $0.7x - 1.4 = -3.5$ is $-3$. This is the solution to the linear equation, and it can be verified by plugging the value of $x$ back into the original equation.
Final Answer
The final answer is $-3$.
Step-by-Step Solution
Here's a step-by-step solution to the problem:
- Add $1.4$ to both sides of the equation: $0.7x - 1.4 + 1.4 = -3.5 + 1.4$
- Simplify the equation: $0.7x = -3.5 + 1.4$
- Add $1.4$ to $-3.5$: $0.7x = -2.1$
- Divide both sides of the equation by $0.7$: $\frac{0.7x}{0.7} = \frac{-2.1}{0.7}$
- Calculate the value of $x$: $x = \frac{-2.1}{0.7}$
- Simplify the fraction: $x = -3$
Frequently Asked Questions
- What is the value of $x$ in the equation $0.7x - 1.4 = -3.5$?
- How do I solve a linear equation?
- What is the step-by-step solution to the problem?
Answer Key
- The value of $x$ in the equation $0.7x - 1.4 = -3.5$ is $-3$.
- To solve a linear equation, you need to isolate the variable by adding or subtracting the same value to both sides of the equation.
- The step-by-step solution to the problem is:
- Add $1.4$ to both sides of the equation: $0.7x - 1.4 + 1.4 = -3.5 + 1.4$
- Simplify the equation: $0.7x = -3.5 + 1.4$
- Add $1.4$ to $-3.5$: $0.7x = -2.1$
- Divide both sides of the equation by $0.7$: $\frac{0.7x}{0.7} = \frac{-2.1}{0.7}$
- Calculate the value of $x$: $x = \frac{-2.1}{0.7}$
- Simplify the fraction: $x = -3$
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form ax + b = c, where a, b, and c are constants, and x is the variable.
Q: How do I solve a linear equation?
A: To solve a linear equation, you need to isolate the variable by adding or subtracting the same value to both sides of the equation. This will eliminate the constant term on the left side of the equation.
Q: What is the first step in solving a linear equation?
A: The first step in solving a linear equation is to add or subtract the same value to both sides of the equation to eliminate the constant term on the left side.
Q: How do I isolate the variable in a linear equation?
A: To isolate the variable in a linear equation, you need to divide both sides of the equation by the coefficient of the variable. This will give you the value of the variable.
Q: What is the coefficient of the variable in a linear equation?
A: The coefficient of the variable in a linear equation is the number that is multiplied by the variable. For example, in the equation 2x + 3 = 5, the coefficient of x is 2.
Q: How do I check my solution to a linear equation?
A: To check your solution to a linear equation, you need to plug the value of the variable back into the original equation and see if it is true.
Q: What is the importance of solving linear equations?
A: Solving linear equations is important because it helps you to understand the relationship between variables and constants in an equation. It also helps you to solve problems in various fields such as science, engineering, and economics.
Q: Can I use a calculator to solve linear equations?
A: Yes, you can use a calculator to solve linear equations. However, it is always a good idea to check your solution by plugging the value of the variable back into the original equation.
Q: How do I simplify a linear equation?
A: To simplify a linear equation, you need to combine like terms and eliminate any unnecessary constants.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2.
Q: Can I solve a linear equation with fractions?
A: Yes, you can solve a linear equation with fractions. However, you need to follow the same steps as solving a linear equation with integers.
Q: How do I solve a linear equation with decimals?
A: To solve a linear equation with decimals, you need to follow the same steps as solving a linear equation with integers. However, you need to be careful when multiplying and dividing decimals.
Q: What is the final answer to the equation 0.7x - 1.4 = -3.5?
A: The final answer to the equation 0.7x - 1.4 = -3.5 is x = -3.
Q: Can I use a graphing calculator to solve a linear equation?
A: Yes, you can use a graphing calculator to solve a linear equation. However, it is always a good idea to check your solution by plugging the value of the variable back into the original equation.
Q: How do I graph a linear equation?
A: To graph a linear equation, you need to use a graphing calculator or a graphing software. You can also use a coordinate plane to graph the equation.
Q: What is the slope of a linear equation?
A: The slope of a linear equation is the ratio of the change in the y-coordinate to the change in the x-coordinate.
Q: How do I find the slope of a linear equation?
A: To find the slope of a linear equation, you need to use the formula m = (y2 - y1) / (x2 - x1), where m is the slope and (x1, y1) and (x2, y2) are two points on the line.
Q: What is the y-intercept of a linear equation?
A: The y-intercept of a linear equation is the point where the line intersects the y-axis.
Q: How do I find the y-intercept of a linear equation?
A: To find the y-intercept of a linear equation, you need to set x = 0 and solve for y.
Q: Can I use a linear equation to model real-world problems?
A: Yes, you can use a linear equation to model real-world problems. Linear equations can be used to model problems such as cost, revenue, and profit.
Q: How do I use a linear equation to model real-world problems?
A: To use a linear equation to model real-world problems, you need to identify the variables and constants in the equation and use them to solve the problem.
Q: What are some examples of real-world problems that can be modeled using linear equations?
A: Some examples of real-world problems that can be modeled using linear equations include:
- Cost and revenue problems
- Profit and loss problems
- Distance and rate problems
- Time and rate problems
- Work and rate problems
Q: Can I use a linear equation to solve a system of equations?
A: Yes, you can use a linear equation to solve a system of equations. However, you need to use a method such as substitution or elimination to solve the system.
Q: How do I use a linear equation to solve a system of equations?
A: To use a linear equation to solve a system of equations, you need to use a method such as substitution or elimination to solve the system.
Q: What are some examples of systems of equations that can be solved using linear equations?
A: Some examples of systems of equations that can be solved using linear equations include:
- Two linear equations with two variables
- Three linear equations with three variables
- Four linear equations with four variables
Q: Can I use a linear equation to solve a quadratic equation?
A: No, you cannot use a linear equation to solve a quadratic equation. However, you can use a method such as factoring or the quadratic formula to solve the quadratic equation.
Q: How do I use a linear equation to solve a quadratic equation?
A: To use a linear equation to solve a quadratic equation, you need to use a method such as factoring or the quadratic formula to solve the quadratic equation.
Q: What are some examples of quadratic equations that can be solved using linear equations?
A: Some examples of quadratic equations that can be solved using linear equations include:
- Quadratic equations with two variables
- Quadratic equations with three variables
- Quadratic equations with four variables
Q: Can I use a linear equation to solve a polynomial equation?
A: No, you cannot use a linear equation to solve a polynomial equation. However, you can use a method such as factoring or the rational root theorem to solve the polynomial equation.
Q: How do I use a linear equation to solve a polynomial equation?
A: To use a linear equation to solve a polynomial equation, you need to use a method such as factoring or the rational root theorem to solve the polynomial equation.
Q: What are some examples of polynomial equations that can be solved using linear equations?
A: Some examples of polynomial equations that can be solved using linear equations include:
- Polynomial equations with two variables
- Polynomial equations with three variables
- Polynomial equations with four variables