Problem 52 Solve the equation. $$1=\frac{... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 52

Solve the equation. $$1=\frac{h}{-5}$$

Short Answer

Expert verified

h = -5

Step by step solution

Understand the Equation

The equation given is $1 = \frac{h}{-5}$. The goal is to solve for $h$.

Isolate the Variable

To isolate $h$, multiply both sides of the equation by $-5$. This removes the denominator.

Perform the Multiplication

Multiply both sides by $-5$: $1 \times -5 = h$.

Simplify

Simplify the left side: $-5 = h$. Therefore, $h = -5$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating Variables

When solving linear equations, a crucial step is isolating the variable we want to find. In the equation given, our variable is $ h $. Isolating a variable means rearranging the equation such that the variable is alone on one side of the equal sign.

Here are some tips for isolating variables:

Identify the variable you need to solve for. In our example, it's $ h $.
Use inverse operations to move other terms or factors to the opposite side.

By carefully performing these steps, you ensure that you maintain the equality of both sides of the equation, guiding you to find the exact value of the variable.

Multiplication in Equations

Multiplication is a commonly used operation when solving equations. If a variable is in a fraction, like in $ 1 = \frac{h}{-5} $, multiplying both sides by the denominator helps eliminate the fraction. This step brings the variable out of the fraction, making it easier to solve.

For example:

Original equation: $ 1 = \frac{h}{-5} $
Multiply both sides by $ -5 $: $ 1 \times -5 = h $

After performing the multiplication, the equation simplifies, isolating the variable. Multiplying both sides of an equation by the same number keeps the equation's balance, an essential principle in algebra.

Simplifying Equations

Simplifying is the process of making an equation easier to understand and solve. After performing operations like multiplication or addition, you often need to combine like terms or reduce the equation to its simplest form.

Consider our example:

After multiplying: $ 1 \times -5 = h $
Simplify: $ -5 = h $

The final step is to rewrite the equation in its simplest form, confirming our variable's value clearly.

By consistently simplifying during each step, you avoid mistakes and end with a clear, accurate solution.

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91影视

Solve the equation. $$1=\frac{h}{-5}$$

Short Answer

Step by step solution

Understand the Equation

Isolate the Variable

Perform the Multiplication

Simplify

Key Concepts

Isolating Variables

Multiplication in Equations

Simplifying Equations

One App. One Place for Learning.

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