Solving Multi-Step Equations Combining Like Terms

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What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve, often involving combining like terms, using the distributive property, and isolating the variable.

Tags

CCSS.8.EE.C.7B

Front

What are like terms?

Back

Like terms are terms in an expression that have the same variable raised to the same power. For example, 3x and 5x are like terms.

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CCSS.6.EE.A.2B

Front

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable. For example, 3x + 5x = 8x.

Tags

CCSS.7.EE.A.1

Front

What is the first step in solving the equation 4 = 7x - 8 - 3x?

Back

The first step is to combine like terms on the right side: 7x - 3x = 4x, so the equation becomes 4 = 4x - 8.

Tags

CCSS.8.EE.C.7B

Front

What is the solution to the equation 4 = 4x - 8?

Back

To solve for x, add 8 to both sides: 4 + 8 = 4x, which simplifies to 12 = 4x. Then divide by 4: x = 3.

Tags

CCSS.7.EE.B.4A

Front

What is the solution to the equation -3x + 8 + 5x = 16?

Back

Combine like terms: 2x + 8 = 16. Then subtract 8 from both sides: 2x = 8. Finally, divide by 2: x = 4.

Tags

CCSS.8.EE.C.7B

Front

How do you isolate the variable in the equation 6x + 3x + 12 = 3?

Back

First, combine like terms: 9x + 12 = 3. Then subtract 12 from both sides: 9x = -9. Finally, divide by 9: x = -1.

Tags

CCSS.7.EE.B.4A

Front

What is the solution to the equation 2x + 7 + 3x = 7?

Back

Combine like terms: 5x + 7 = 7. Subtract 7 from both sides: 5x = 0. Then divide by 5: x = 0.

Tags

CCSS.8.EE.C.7B

Front

What is the solution to the equation -2x + 14 + 8x = -10?

Back

Combine like terms: 6x + 14 = -10. Subtract 14 from both sides: 6x = -24. Then divide by 6: x = -4.

Tags

CCSS.8.EE.C.7B

Front

What does it mean to 'isolate the variable'?

Back

Isolating the variable means manipulating the equation so that the variable is on one side by itself, making it easier to solve.

Tags

CCSS.7.EE.B.4A