Solving Multi-Step Linear Equations and Inequalities

Front

Define a multi-step linear equation.

Back

A multi-step linear equation is an equation that requires more than one step to isolate the variable and solve for its value, often involving operations such as addition, subtraction, multiplication, and division.

Front

What is the first step in solving the equation -8x - 8 + 3(x - 2) = -3x + 2?

Back

The first step is to distribute the 3 to the terms inside the parentheses: -8x - 8 + 3x - 6 = -3x + 2.

Front

Solve the equation: 3(x-4) = -3. What is x?

Back

x = 3.

Front

What does the inequality 6x + 10 > 5x - 12 represent?

Back

It represents a condition where the value of 6x + 10 is greater than the value of 5x - 12.

Front

Solve the inequality: 6x + 10 > 5x - 12. What is x?

Back

x > -22.

Front

Back

x = \frac{1}{6}.

Front

Back

Combine like terms and solve for x to find x = 2.

Front

What is the definition of a linear inequality?

Back

A linear inequality is an inequality that involves a linear function, which can be expressed in the form ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c.

Front

What is the significance of the solution set in inequalities?

Back

The solution set represents all possible values of the variable that satisfy the inequality.

Front

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

Back

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