Solve for h 1.8=2.1h-5.7-4.6h
The given problem is a linear equation which involves solving for the variable h. The equation presented is 1.8 = 2.1h - 5.7 - 4.6h. The task involves combining like terms, both the constants and the coefficients of h, and rearranging the equation such that h is isolated on one side of the equation. To find the value of h, one would need to perform algebraic operations like addition, subtraction, and division following the principles of equation balancing, where whatever operation is done on one side of the equation is also done on the other side to maintain equality.
$1.8 = 2.1 h - 5.7 - 4.6 h$
Answer
Solution:
Step 1: Arrange the equation
Express the equation in the form $2.1h - 4.6h - 5.7 = 1.8$.
Step 2: Combine like terms
Combine $2.1h$ and $-4.6h$ to get $-2.5h - 5.7 = 1.8$.
Step 3: Isolate the variable term
Shift all non-variable terms to the opposite side of the equation.
Step 3.1: Add 5.7 to both sides
Perform the operation $-2.5h = 1.8 + 5.7$.
Step 3.2: Calculate the sum
Compute the result of $1.8 + 5.7$ to obtain $-2.5h = 7.5$.
Step 4: Solve for the variable
Divide the equation by the coefficient of the variable to find its value.
Step 4.1: Divide by -2.5
Apply the division $\frac{-2.5h}{-2.5} = \frac{7.5}{-2.5}$.
Step 4.2: Simplify the equation
Eliminate the common factor to isolate $h$.
Step 4.2.1: Eliminate the common factor
Execute the cancellation $\frac{\cancel{-2.5}h}{\cancel{-2.5}} = \frac{7.5}{-2.5}$.
Step 4.2.1.1: Simplify the left side
Reduce the left side to $h$.
Step 4.2.1.2: Compute the division
Calculate $h = \frac{7.5}{-2.5}$.
Step 4.3: Obtain the final result
Finalize the calculation to determine $h = -3$.
Knowledge Notes:
To solve the given equation $1.8 = 2.1h - 5.7 - 4.6h$, we follow a systematic approach:
Rearrange the Equation: We start by rewriting the equation in a standard form, placing all terms involving the variable on one side and the constants on the other.
Combine Like Terms: We then combine terms that contain the same variable by adding or subtracting the coefficients.
Isolate the Variable: To solve for the variable, we move all terms not containing the variable to the other side of the equation. This is usually done by performing inverse operations such as addition or subtraction.
Simplify: Once the variable is isolated, we simplify the equation by performing any necessary arithmetic operations.
Divide by the Coefficient: If the variable term has a coefficient other than 1, we divide the entire equation by that coefficient to solve for the variable.
Check the Solution: It is always a good practice to check the solution by substituting it back into the original equation to ensure that it satisfies the equation.
In this specific problem, we use algebraic manipulation to isolate $h$ and solve for its value. The equation involves combining like terms and performing arithmetic operations such as addition, subtraction, and division.
