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Chapter 2: Problem 58

Solve equation, and check your solution \(8 x+3 x=121\)

Short Answer

Expert verified
x = 11

Step by step solution

01

Combine like terms

Add the coefficients of the variable x in the equation. Here, you have two terms containing x: 8x and 3x. So, combine them: \[8x + 3x = 11x\].
02

Simplify the equation

Rewrite the equation with the combined like terms. The equation now becomes: \[11x = 121\].
03

Solve for x

Divide both sides of the equation by 11 to isolate x: \[x = \frac{121}{11} = 11\].
04

Check the solution

Substitute x back into the original equation to verify the solution. Original equation: \[8x + 3x = 121\]. Substitute x = 11:\[8(11) + 3(11) = 88 + 33 = 121\]. Since the left-hand side equals the right-hand side, the solution x = 11 is correct.

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Key Concepts

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

Combining like terms
In algebra, it's important to simplify equations to make them easier to solve. One way to do this is by combining like terms. Like terms are terms that have the same variable raised to the same power. In the exercise, we see:
  • 8x + 3x
Both terms have the variable x raised to the power of 1. We combine them by adding their coefficients:
  • 8 + 3 = 11
Hence, our equation simplifies to: \[8x + 3x = 11x \] This means we have only one term involving x, which makes the next steps much simpler.
Isolating variables
To solve for a variable, you need to get the variable on one side of the equation by itself. This is called isolating the variable.
In our simplified equation \[11x = 121 \] the goal is to get x alone on one side. You do this by performing the same operation on both sides of the equation. Here, you divide both sides by 11:
\[ \frac{11x}{11} = \frac{121}{11} \] Simplifying both sides, we get:
  • x = 11
Now we have isolated x and found its value. This process ensures that x is the only term on one side of the equation, making it straightforward to see its value.
Verifying solutions
Just finding a solution isn't enough; you should always verify it to ensure it's correct. To do this, substitute the value back into the original equation and check if both sides are equal.
The original equation is:
\[8x + 3x = 121 \] Substitute the found value of x, which is 11:
  • 8(11) + 3(11) = 88 + 33 = 121
Both sides match, confirming that our solution x = 11 is indeed correct. Verifying solutions is a crucial step as it ensures there are no mistakes made during the solving process. This habit can help avoid errors and solidify your understanding of algebraic techniques.

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