Question

Solve each equation. Check your answer. $$ 4 x-5=2(2 x+1) $$

   Solve each equation. Check your answer.
$$
4 x-5=2(2 x+1)
$$

Algebra 1 Common Core

Algebra 1 Common Core

Randall I.… 1st Edition

Chapter 2, Problem 4

Instant Answer

Solved by Expert Thomas Emment

03/22/2020

Step 1

This gives us: $$ 4x - 5 = 2(2x + 1) \Rightarrow 4x - 5 = 4x + 2 $$ Show more…

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Solve each equation. Check your answer. $$ 4 x-5=2(2 x+1) $$

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Key Concepts

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The goal is to determine the value of the variable that makes the equation true. This concept is central to algebra and involves methods like isolating the variable and maintaining equality on both sides of the equation.

Distributive Property

The distributive property allows you to multiply a single term by every term within a parenthesis, which simplifies expressions and makes it easier to combine like terms. It is especially useful in simplifying equations where expressions are multiplied by coefficients, providing a systematic way to eliminate parentheses.

Combining Like Terms

Combining like terms involves adding or subtracting coefficients of terms that have the same variable raised to the same power. This step simplifies the equation into a more manageable form and is crucial in isolating the variable and solving linear equations efficiently.

Solution Verification

Solution verification is the process of substituting the found value back into the original equation to ensure that both sides of the equation are equal. This step confirms that the solution is correct and that no errors were made during the algebraic manipulation.

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