Solve for h -8=9-5h

The given problem is an algebraic equation where you are asked to solve for the variable 'h'. The equation is stated as "-8 = 9 - 5h". You are expected to manipulate the equation using algebraic rules to isolate 'h' and find its value. This typically involves performing operations such as adding or subtracting the same quantity from both sides of the equation, or dividing or multiplying both sides by the same number, with the goal of obtaining 'h' by itself on one side of the equation, yielding its solution.

$- 8 = 9 - 5 h$

Answer

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Solution:

Step 1: Rewrite the Equation

Start by expressing the equation in the standard form: $- 5 h + 9 = - 8$ .

Step 2: Isolate the Variable

Move all terms not including $h$ to the opposite side of the equation.

Step 2.1: Subtract 9 from Both Sides

Perform subtraction of $9$ from both sides to get $- 5 h = - 8 - 9$ .

Step 2.2: Combine Like Terms

Combine the constants on the right side to simplify: $- 5 h = - 17$ .

Step 3: Solve for $h$

Divide the entire equation by the coefficient of $h$ to find its value.

Step 3.1: Divide by -5

Apply division to each term: $\frac{- 5 h}{- 5} = \frac{- 17}{- 5}$ .

Step 3.2: Simplify the Equation

Reduce the equation to its simplest form.

Step 3.2.1: Eliminate Common Factors

Remove the common factor of $- 5$ : $h = \frac{- 17}{- 5}$ .

Step 3.2.2: Simplify the Variable Term

Simplify to get the value of $h$ : $h = \frac{- 17}{- 5}$ .

Step 3.3: Simplify the Constant Term

Recognize that dividing two negative numbers yields a positive result: $h = \frac{17}{5}$ .

Step 4: Present the Result in Various Forms

The solution can be expressed in different ways.

Exact Form: $h = \frac{17}{5}$

Decimal Form: $h = 3.4$

Mixed Number Form: $h = 3 \frac{2}{5}$

Solution:"The variable $h$ is isolated and solved for by first rearranging the equation, then simplifying and dividing by the coefficient of $h$ . The final solution is presented in exact, decimal, and mixed number forms."

Knowledge Notes:

Equation Rearrangement: To solve for a variable, it's often necessary to rearrange the equation to isolate the variable on one side.
Combining Like Terms: This involves simplifying expressions by adding or subtracting constants or coefficients.
Division to Isolate Variable: When a variable is multiplied by a coefficient, division is used to isolate the variable.
Negative Division: Dividing two negative numbers results in a positive number.
Multiple Representations: Solutions can be represented in different forms, such as fractions, decimals, or mixed numbers, depending on the context or preference.