Solving linear equations with CLT and distributive property

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does it mean to combine like terms in an equation?

Back

Combining like terms involves simplifying an expression by adding or subtracting terms that have the same variable raised to the same power.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you solve a linear equation using the distributive property?

Back

To solve a linear equation using the distributive property, distribute the term outside the parentheses to each term inside, then combine like terms and isolate the variable.

Front

What is the first step in solving the equation -15 + 3x - 7x = -43?

Back

The first step is to combine like terms on the left side of the equation, which results in -15 - 4x = -43.

Front

How do you isolate the variable x in the equation 4x + 5x + 7 - 3x + 5 = -18?

Back

First, combine like terms to simplify the equation to 6x + 12 = -18, then subtract 12 from both sides and divide by 6 to find x.

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What is the solution to the equation -2(x + 5) = 8?

Back

The solution is x = -9, found by distributing -2, combining like terms, and isolating x.

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How do you solve the equation 3x + 2(4x - 4) = 3?

Back

Distribute 2 to get 3x + 8x - 8 = 3, combine like terms to get 11x - 8 = 3, then isolate x to find x = 1.

Front

What is the solution to the equation 8v - 4(v + 8) = 8?

Back

The solution is v = 10, found by distributing -4, combining like terms, and isolating v.

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What is the importance of checking your solution in a linear equation?

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Checking your solution ensures that the value you found satisfies the original equation, confirming its correctness.