Question

Solve for the indicated variable. $$ 4(x-3)=2(x+6) $$

   Solve for the indicated variable.
$$
4(x-3)=2(x+6)
$$

Algebra and Trigonometry

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 1, Problem 19

Instant Answer

Solved by Expert Amy Jiang

06/30/2020

Step 1

On the left side, distribute 4 to both terms inside the parentheses: \[ 4(x - 3) = 4x - 12 \] On the right side, distribute 2 to both terms inside the parentheses: \[ 2(x + 6) = 2x + 12 \] Show more…

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Solve for the indicated variable. $$ 4(x-3)=2(x+6) $$

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Key Concepts

Inverse Operations

Inverse operations involve using operations that reverse the effect of another operation, such as addition with subtraction or multiplication with division. This technique is essential in solving equations, as it allows you to isolate the variable by systematically undoing applied operations.

Linear Equations

Linear equations involve making an equation in which the highest exponent of the variable is one. They represent straight-line relationships when graphed and can be solved by systematically performing algebraic operations to isolate the unknown variable.

Distributive Property

The distributive property is a key algebraic principle which allows you to multiply a single term by each term within a parenthesis. It transforms expressions like a(b + c) into ab + ac, which is essential for eliminating parentheses and simplifying equations.

Combining Like Terms

Combining like terms is the process of simplifying expressions by adding or subtracting coefficients of terms that have the same variable components. This reduces the complexity of expressions, allowing equations to be simplified and solved more easily.

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