Question

Solve each equation. $$ 3(x+1)+5=3 x+2 $$

   Solve each equation.
$$
3(x+1)+5=3 x+2
$$

Intermediate Algebra

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 2, Problem 37

Instant Answer

Solved by Expert Xiaomeng Zhang

07/16/2020

Step 1

Step 1: First, we distribute the 3 in the left side of the equation: $$ 3x + 3 + 5 = 3x + 2 $$ Show more…

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Solve each equation. $$ 3(x+1)+5=3 x+2 $$

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Key Concepts

Isolating the Variable

Isolating the variable means rearranging the equation so that the variable appears on one side and all the constant terms on the other. This is achieved through inverse operations such as addition, subtraction, multiplication, or division, and is the final step in solving for the unknown in a linear equation.

Combining Like Terms

Combining like terms involves adding or subtracting coefficients of terms that contain the same variable or are constants. This process simplifies the equation by reducing it to a form where the variable terms and constant terms are fully consolidated, which is crucial for further operations.

Distributive Property

The distributive property allows you to multiply a single term across terms inside parentheses, expressed as a(b + c) = ab + ac. This property is essential for eliminating parentheses and simplifying equations before further manipulations.

Linear Equations

Linear equations are equations where each term is either a constant or the product of a constant and a single variable raised to the first power. They have at most one solution, and solving them involves applying several fundamental algebraic techniques such as distribution and combining like terms to isolate the variable.

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