What is the first step to solving a long equation like [tex]$3 x+5+8 x-12=12 x+2-13-3 x$[/tex] ?
A. Combine like terms
B. Subtract the numbers with the variables
C. Add
D. Move the variables over to one side
Answer (2)
Combine like terms on the left side of the equation: 3 x + 8 x = 11 x and 5 − 12 = − 7 , resulting in 11 x − 7 .
Combine like terms on the right side of the equation: 12 x − 3 x = 9 x and 2 − 13 = − 11 , resulting in 9 x − 11 .
The simplified equation is 11 x − 7 = 9 x − 11 .
The first step to solving the equation is to combine like terms. C o mbin e l ik e t er m s
Explanation
Identify Like Terms The equation we need to solve is 3 x + 5 + 8 x − 12 = 12 x + 2 − 13 − 3 x . To solve this equation, we need to simplify both sides by combining like terms. This means grouping together the terms with 'x' and the constant terms (numbers).
Combine Like Terms on the Left Side On the left side of the equation, we have 3 x and 8 x as like terms, and 5 and − 12 as like terms. Combining these, we get:
3 x + 8 x = 11 x 5 − 12 = − 7
So, the left side simplifies to 11 x − 7 .
Combine Like Terms on the Right Side On the right side of the equation, we have 12 x and − 3 x as like terms, and 2 and − 13 as like terms. Combining these, we get:
12 x − 3 x = 9 x 2 − 13 = − 11
So, the right side simplifies to 9 x − 11 .
State the First Step Now our equation looks like this:
11 x − 7 = 9 x − 11
The first step to solving the original equation was to combine like terms on each side.
Final Answer Therefore, the first step to solving the equation 3 x + 5 + 8 x − 12 = 12 x + 2 − 13 − 3 x is to combine like terms.
Examples
Imagine you're balancing a budget. On one side, you have income from different sources and expenses. Combining like terms is like adding up all your income and then subtracting all your expenses to see your net balance. Similarly, in equations, combining like terms simplifies the equation, making it easier to solve for the unknown variable.
The first step to solving the equation 3 x + 5 + 8 x − 12 = 12 x + 2 − 13 − 3 x is to combine like terms on both sides of the equation. This involves grouping and simplifying terms that contain the variable x and the constant terms. Therefore, the correct answer is A. Combine like terms.
;
