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Chapter 15: Problem 28

Solve. $$ 18=9-(3-x) $$

Short Answer

Expert verified
x = 12

Step by step solution

01

Expand the Equation

Remove the parentheses by distributing the minus sign: \( 18 = 9 - 3 + x \)
02

Simplify the Right Side

Combine like terms on the right side of the equation: \( 18 = 6 + x \)
03

Isolate the Variable

Subtract 6 from both sides to isolate \( x \): \( 18 - 6 = x \)
04

Simplify

Perform the subtraction: \( 12 = x \)

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Key Concepts

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

Distributive Property
The distributive property allows us to remove parentheses in an equation by distributing a multiplier or, in this case, by dealing with a minus sign that impacts the terms inside the parentheses. In the given problem, the equation is:
18 = 9 - (3-x).
Here, the minus sign before the parentheses needs to be distributed to both 3 and -x, effectively changing both their signs. Distributing the minus sign gives us:
18 = 9 - 3 + x.
This step ensures we distribute any operation affecting multiple terms correctly, which simplifies further solving.
Combining Like Terms
Once we have distributed any multipliers or signs, the next step is to combine like terms. Like terms are terms that have the same variables raised to the same power. In our simplified equation, we have:
18 = 9 - 3 + x.
The constants 9 and -3 are like terms because they are both numbers without variables. By combining these, we get:
18 = 6 + x.
Combining like terms helps reduce the equation to fewer terms, making it easier to solve.
Isolating Variables
Isolating the variable means getting the variable by itself on one side of the equation. In our equation, we now have:
18 = 6 + x.
To isolate x, we need to remove the 6 from the right side. We do this by subtracting 6 from both sides of the equation:
18 - 6 = x.
Performing the operation gives us:
12 = x.
Isolating the variable is crucial because it allows us to directly determine its value.
Simplifying Equations
Simplifying equations involves performing all possible arithmetic operations to find the value of the variable. After isolating the variable in our last step, we have:
18 - 6 = x.
Simplifying this subtraction gives us:
12 = x.
Now we have our solution in its simplest form, showing that x equals 12. Simplifying ensures that we reach the most straightforward and accurate solution possible for the given equation.

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