Problem 18 Solve the equation using the mul... [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 18

Solve the equation using the multiplication or division properties of equality. $$-h=-17$$

Short Answer

Expert verified

h = 17

Step by step solution

Understand the Equation

Begin by reviewing the equation: -h = -17

Isolate the Variable

To solve for h, isolate the variable by dividing both sides of the equation by -1: -h / (-1) = -17 / (-1)

Simplify Both Sides

Simplify the division on both sides: h = 17

Verify the Solution

To verify, substitute h back into the original equation: -h = -17 Substituting h = 17 into the equation gives -17 = -17, which confirms that the solution is correct.

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Key Concepts

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

multiplication property of equality

When you multiply both sides of an equation by the same non-zero value, the equality remains true. This concept is known as the multiplication property of equality.
Imagine you have an equation like $a = b$. If you multiply both sides by a number, say $c$, you get $ac = bc$.
For example, if $2x = 10$, multiplying both sides by $1/2$ gives you $(1/2) * 2x = (1/2) * 10$, simplifying to $x = 5$.
This helps in solving equations and isolating variables.

division property of equality

The division property of equality states that if you divide both sides of an equation by the same non-zero number, the equality remains the same. This property is especially useful when dealing with linear equations.
For instance, let's solve the equation $-h = -17$. We need to isolate $h$. We achieve this by dividing both sides by $-1$.
Thus, $-h / (-1) = -17 / (-1)$, simplifying to $h = 17$.
This makes it easier to solve equations where the variable is multiplied by a coefficient.

isolating the variable

Isolating the variable means getting the variable by itself on one side of the equation. This is the primary goal when solving equations.
For the equation $-h = -17$, to isolate $h$, we divide both sides by $-1$. The equation transforms to $h = 17$.
By isolating the variable, we reveal its value, making it easier to understand and solve the equation.

verifying solutions

Verifying solutions is the process of checking if the obtained solution satisfies the original equation. This step ensures that your solution is correct and reduces errors.
In our case, we found $h = 17$. To verify, substitute $h = 17$ back into the original equation $-h = -17$:
Replace $h$ with 17: $-17 = -17$, proving the solution is correct.
Always double-check your solutions by plugging them back into the equation!

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91影视

Solve the equation using the multiplication or division properties of equality. $$-h=-17$$

Short Answer

Step by step solution

Understand the Equation

Isolate the Variable

Simplify Both Sides

Verify the Solution

Key Concepts

multiplication property of equality

division property of equality

isolating the variable

verifying solutions

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