3.6 - 3.8 Review

Front

What is the process to solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation by performing inverse operations (addition, subtraction, multiplication, division) on both sides until the variable is alone.

Front

What does it mean if an equation has one solution?

Back

An equation has one solution if there is exactly one value for the variable that makes the equation true.

Front

How do you determine if an equation has no solution?

Back

An equation has no solution if the variable cancels out and results in a false statement, such as 0 = 5.

Front

What is the significance of the coefficient in a linear equation?

Back

The coefficient is the number multiplied by the variable and determines the rate of change of the variable in the equation.

Front

What is the first step in solving the equation 6g - 9 - 8g = 1/2(4g - 10)?

Back

The first step is to simplify both sides of the equation, combining like terms and distributing any factors.

Front

How do you solve for n in the equation 10 + 2n = 8n - 2n + 10?

Back

Combine like terms on both sides to simplify the equation, then isolate n by moving all n terms to one side.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the solution to the equation 3b + 12 - 6b = -9?

Back

The solution is b = 7, found by combining like terms and isolating b.

Front

How do you check if your solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is the result of solving the equation 2x - 5 = 3x + 4?

Back

The result is x = -9, found by isolating x on one side of the equation.