Solving Equations with Distributing and Combining Like Terms

Front

What is the process of distributing in algebra?

Back

Distributing involves multiplying a single term by each term inside a set of parentheses. For example, in 3(2x + 4), you would multiply 3 by 2x and 3 by 4, resulting in 6x + 12.

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What are like terms in algebra?

Back

Like terms are terms that have the same variable raised to the same power. For example, 2x and 3x are like terms, while 2x and 3y are not.

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How do you combine like terms?

Back

To combine like terms, you add or subtract the coefficients of the terms that are alike. For example, 2x + 3x = 5x.

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What is the first step in solving the equation 7x - 4x = 27?

Back

The first step is to combine like terms on the left side: 7x - 4x = 3x, so the equation becomes 3x = 27.

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What is the solution to the equation 6 - 3a = 21?

Back

To solve for a, first subtract 6 from both sides to get -3a = 15, then divide by -3 to find a = -5.

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How do you solve the equation 7(4x + 3) + 5 = -58?

Back

First, distribute 7: 28x + 21 + 5 = -58. Then combine like terms: 28x + 26 = -58. Subtract 26 from both sides to get 28x = -84, and divide by 28 to find x = -3.

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What is the solution to the equation 6x - 5 + 7x = 34?

Back

Combine like terms: 6x + 7x = 13x, so the equation becomes 13x - 5 = 34. Add 5 to both sides to get 13x = 39, then divide by 13 to find x = 3.

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How do you solve the equation 2n + 3n + 7 = -43?

Back

Combine like terms: 2n + 3n = 5n, so the equation becomes 5n + 7 = -43. Subtract 7 from both sides to get 5n = -50, then divide by 5 to find n = -10.

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What does it mean to isolate a variable in an equation?

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Isolating a variable means rearranging the equation so that the variable is on one side by itself. For example, in the equation 2x + 3 = 7, you would subtract 3 from both sides to isolate 2x.

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What is the importance of checking your solution in an equation?

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Checking your solution ensures that the value you found satisfies the original equation. This helps confirm that no mistakes were made during the solving process.