Solve for z -6z+1=-4-7z
Brief Explanation:
The question provided is a basic linear equation in one variable, which in this case is 'z'. The equation is presented in the form of -6z + 1 = -4 - 7z, and the task is to find the value of 'z' that satisfies this equation. To solve for 'z', you would typically isolate the variable on one side of the equation, which involves performing algebraic manipulations such as adding or subtracting terms on both sides to cancel out terms and get 'z' by itself. Once 'z' is isolated, the value that makes the equation true can be determined.
$- 6 z + 1 = - 4 - 7 z$
Answer
Solution:
Step 1
Consolidate all the $z$ terms on one side of the equation.
Step 1.1
Add $7z$ to each side to move the $z$ term from the right to the left.$-6z + 1 + 7z = -4 + 7z$
Step 1.2
Combine like terms involving $z$.$1z + 1 = -4$
Step 2
Isolate the variable $z$ by moving constant terms to the opposite side.
Step 2.1
Subtract $1$ from both sides to eliminate the constant term on the left.$z = -4 - 1$
Step 2.2
Calculate the sum of the constants on the right side.$z = -5$
Knowledge Notes:
The problem involves solving a simple linear equation for the variable $z$. The process of solving linear equations typically involves isolating the variable on one side of the equation while keeping the equation balanced. This is done through the use of inverse operations, such as addition and subtraction, as well as multiplication and division when necessary.
Here are the relevant knowledge points and detailed explanations:
Moving terms with the variable: To solve for $z$, we need to get all the terms with $z$ on one side of the equation. This is done by adding or subtracting terms on both sides of the equation, ensuring that the equation remains balanced.
Combining like terms: After moving the terms, we combine like terms, which are terms that have the same variable raised to the same power. In this case, $-6z$ and $7z$ are like terms and can be added together to get $1z$ or simply $z$.
Isolating the variable: The next step is to isolate the variable on one side of the equation. This is done by moving the constant terms to the opposite side using subtraction or addition.
Solving the equation: Once the variable is isolated, we perform the arithmetic operations required to find the value of the variable. In this case, we subtract $1$ from $-4$ to find that $z = -5$.
Checking the solution: It is always good practice to check the solution by substiting the value of $z$ back into the original equation to ensure that both sides are equal. In this case, substituting $z = -5$ into the original equation $-6z + 1 = -4 - 7z$ should result in a true statement.
The process described above is a systematic approach to solving linear equations and is foundational for algebra.
