Solve each equation. Check the result. See Example 7 . 3(x-4)+3 x=2(x+10)

Name: Problem 43, Chapter 3: Prealgebra
Uploaded: 2020-07-20T17:27:19-08:00
Duration: 43 s
Channel: Amy Jiang
Description: Solve each equation. Check the result. See Example 7 . 3(x-4)+3 x=2(x+10)

step 1 Okay, so let's start by multiplying out of 3 and a 2. So we have 3x minus 12 plus 3x. That's equ

Solve each equation. Check the result. See Example 7 ....

Key Concepts

Verification of Solutions

Verification of solutions is a critical step in solving equations, where the proposed solution is substituted back into the original equation to confirm that it satisfies the equation. Checking the result ensures that no errors have been made during the manipulation of the equation, and that the solution accurately balances both sides of the equation.

Isolating the Variable

Isolating the variable is a strategy used in solving equations where all terms containing the variable are moved to one side of the equation and all constant terms to the other. This process involves performing the same operation on both sides of the equation to maintain equality. The goal is to rewrite the equation in a form where the variable appears alone on one side, thereby revealing its value.

Combining Like Terms

Combining like terms is the process of simplifying algebraic expressions by adding or subtracting terms that have the same variable raised to the same power. By merging these similar terms, the equation is simplified, which makes it easier to isolate the variable and solve the equation efficiently.

Distributive Property

The distributive property is a fundamental algebraic property used to multiply a single term across terms inside a parenthesis. It allows for the expansion of expressions such as a(b + c) into ab + ac. This property is essential for simplifying algebraic expressions and is one of the first steps in solving equations where terms inside parentheses need to be expanded.

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 solution involves finding the value of the variable that makes the equation true. Linear equations are characterized by their highest power of the variable being one, which allows them to be represented as a straight line when graphed.

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