Solving multi-step problems using linear equations in one variable

Front

What is a linear equation in one variable?

Back

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where a and b are constants and x is the variable.

Front

What does it mean if an equation has one solution?

Back

It means there is exactly one value of the variable that satisfies the equation.

Front

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

Back

It means that there are countless values of the variable that satisfy the equation, often resulting from an identity.

Front

What does it mean if an equation has no solution?

Back

It means there is no value of the variable that can satisfy the equation, often resulting from a contradiction.

Front

How do you determine the number of solutions for the equation -25z + 1 + 35z = 10z + 1?

Back

Combine like terms: 10z + 1 = 10z + 1, which simplifies to an identity, indicating infinitely many solutions.

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How do you determine the number of solutions for the equation -3(2x+5)=-15?

Back

Distribute and simplify: -6x - 15 = -15, which simplifies to -6x = 0, giving one solution: x = 0.

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What does the equation 2 = X indicate about the number of solutions?

Back

It indicates one solution, specifically X = 2.

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What does the equation 4 = 4 indicate about the number of solutions?

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It indicates infinitely many solutions, as it is always true.

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How do you solve the equation 8x - 3 = 3x - 3?

Back

Combine like terms: 5x = 0, giving one solution: x = 0.

Front

What is the first step in solving a multi-step linear equation?

Back

The first step is to simplify both sides of the equation by combining like terms and eliminating parentheses.