In order to determine the value that solves the equation 5-4x = 3, we need to isolate the variable x and perform the necessary operations. Let’s solve this equation step by step.
Solution:
1. Start with the given equation: 5-4x = 3.
2. Subtract 5 from both sides of the equation to isolate the term with x: 5-5-4x = 3-5, which simplifies to -4x = -2.
3. Divide both sides of the equation by -4 to solve for x: -4x/-4 = -2/-4, leading to x = 1/2.
The solution to the equation 5-4x = 3 is x = 1/2. This means that when x equals 1/2, the equation is satisfied and the left side (5-4x) equals the right side (3).
Frequently Asked Questions:
Q: How do you solve linear equations?
A: To solve a linear equation, you need to perform operations to isolate the variable on one side of the equation.
Q: What is the first step in solving linear equations?
A: The first step is to simplify both sides of the equation as much as possible by removing parentheses, combining like terms, and performing operations.
Q: How do you isolate a variable in an equation?
A: You isolate a variable in an equation by performing inverse operations on both sides of the equation. For example, if the variable is multiplied by a number, you divide by that number to isolate it.
Q: How many solutions can a linear equation have?
A: A linear equation can have one solution, infinitely many solutions, or no solutions.
Q: What does it mean if an equation has no solution?
A: It means that there are no values that satisfy the equation. In other words, there is no solution that makes both sides of the equation equal.
Q: What does it mean if an equation has infinitely many solutions?
A: It means that any value would satisfy the equation. In other words, the equation is always true regardless of the value you choose for the variable.
Q: Can a linear equation have more than one solution?
A: Yes, a linear equation can have infinitely many solutions if the variable is eliminated during the solving process.
Q: How can I check if my solution is correct?
A: To verify if your solution is correct, substitute the value you found for the variable back into the original equation and see if both sides are equal.
Q: What other types of equations are there?
A: Besides linear equations, there are quadratic equations, exponential equations, logarithmic equations, and many more.
Q: Can negative numbers be solutions to equations?
A: Yes, negative numbers can indeed be solutions to equations. The solution can be positive, negative, or zero, depending on the specific equation.
Q: What if I get different solutions when solving an equation?
A: If you get different solutions, it is essential to revise your work and verify each step to ensure accuracy. Mistakes in calculations or algebraic manipulations might result in incorrect solutions.
Q: Can fractions or decimals be solutions to equations?
A: Absolutely! Equations can have solutions that are fractions, decimals, or mixtures of both. These solutions are as valid as whole numbers.
In conclusion, the value that solves the equation 5-4x = 3 is x = 1/2. Remember to double-check your work and ensure that your solution satisfies the original equation. Solving equations is a fundamental skill in mathematics and is used in a wide range of fields including physics, engineering, economics, and more.