Multistep Equations and INequalities

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What is a multistep equation?

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A multistep equation is an equation that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, and division.

Tags

CCSS.7.EE.B.4A

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How do you determine if an equation has one solution, no solutions, or infinitely many solutions?

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To determine the number of solutions, simplify the equation. If you end up with a true statement (e.g., 0=0), there are infinitely many solutions. If you get a false statement (e.g., 0=5), there are no solutions. If you find a specific value for the variable, there is one solution.

Tags

CCSS.8.EE.C.7A

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Solve the equation: 5x + 4 = 2x + 4

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x = 0 (One solution)

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Solve the inequality: 77 ≤ 5 + 8n

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n ≥ 9 (Graph the solution on a number line starting from 9 to the right)

Tags

CCSS.7.EE.B.4B

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What does it mean if an equation has no solutions?

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An equation has no solutions when the simplified form leads to a contradiction, such as 0 = 5.

Tags

CCSS.8.EE.C.7A

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Solve the equation: 4 - 3x = -3(x - 5) - 7

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No solution (the equation simplifies to a contradiction).

Tags

CCSS.8.EE.C.7A

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Tags

CCSS.6.EE.B.8

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Solve the equation: 3y + 6 + 4y - 7 = -8

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y = -1 (One solution)

Tags

CCSS.8.EE.C.7B

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What does it mean if an equation has infinitely many solutions?

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An equation has infinitely many solutions when the simplified form results in a true statement for all values of the variable, such as 0 = 0.

Tags

CCSS.8.EE.C.7A

Front

Solve the equation: 2x + 4 = 2x + 4

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Infinitely many solutions (the equation is always true).

Tags

CCSS.8.EE.C.7A