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Chapter 8: Problem 164

Solve the linear equation using the general strategy. $$8=4(x-3)$$

Short Answer

Expert verified
x = 5

Step by step solution

01

Distribute

Distribute the 4 on the right-hand side of the equation: 8 = 4(x - 3) You get: 8 = 4x - 12
02

Isolate the variable term

Move the constant term (-12) to the left-hand side by adding 12 to both sides: 8 + 12 = 4x - 12 + 12 This simplifies to: 20 = 4x
03

Solve for x

Divide both sides of the equation by 4 to solve for x: \(\frac{20}{4} = \frac{4x}{4}\) This simplifies to: x = 5

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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 is a helpful tool in algebra. It means you can distribute, or multiply, one number across terms inside parentheses. Here's a simple example: if you have \(a(b+c)\), you can distribute \(a\) to both \(b\) and \(c\). This gives you \(ab + ac\).
Let's use the distributive property in our exercise:
Given equation: \(8=4(x-3)\)
Distribute the 4 to both \(x\) and \(-3\):
We get \(8=4x-12\).
This step simplifies the equation, making it easier to solve.
isolating the variable
Isolating the variable is an essential step in solving equations. It means moving all terms with the variable to one side and all constants to the other.
In our exercise, after using the distributive property, we have \(8=4x-12\).
To isolate \(4x\), we need to move \(-12\) to the left side. We do this by adding 12 to both sides of the equation:
\(8 + 12 = 4x - 12 + 12\).
This gives us \(20 = 4x\).
Now, the variable term is isolated.
solving for x
After isolating the variable term, the next step is to solve for the variable.
From our previous step, we now have \(20 = 4x\).
To find \(x\), we need to get rid of the 4 multiplying \(x\) by dividing both sides of the equation by 4:
\(\frac{20}{4} = \frac{4x}{4}\).
This simplifies to \(x = 5\).
So, the solution to the equation is \(x = 5\). Always remember to check your work by plugging the solution back into the original equation.

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