Question

Solve each equation. $$ 3 x+2(x+4)=5(x+1)+3 $$

   Solve each equation.
$$
3 x+2(x+4)=5(x+1)+3
$$

Intermediate Algebra

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 2, Problem 48

Instant Answer

Solved by Expert Xiaomeng Zhang

07/16/2020

Step 1

Step 1: First, we distribute the numbers outside the parentheses on both sides of the equation: $$ 3x + 2x + 8 = 5x + 5 + 3 $$ Show more…

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Solve each equation. $$ 3 x+2(x+4)=5(x+1)+3 $$

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Key Concepts

Linear Equations

A linear equation is an equation in which the highest power of the variable is one. Solving linear equations involves finding the value of the variable that makes the equation true. These equations represent straight lines when graphed and are a fundamental concept in algebra.

Distributive Property

The distributive property allows you to multiply a single term by each term inside a set of parentheses. It is expressed as a(b + c) = ab + ac. This property is essential in algebra for expanding expressions and simplifying equations.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This process simplifies algebraic expressions and makes it easier to solve equations by reducing the number of terms.

Isolating the Variable

Isolating the variable refers to the method of rearranging an equation so that the variable appears on one side and all constant terms on the other. This typically involves using inverse operations such as addition, subtraction, multiplication, and division to solve for the variable.

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