Topic 8 Test: Equations

Front

What is the first step to solve the equation 3(3x - 6) = 18?

Back

Distribute the 3 to both terms inside the parentheses: 9x - 18 = 18.

Front

How do you isolate x in the equation -2(5x - 1) = -38?

Back

First, distribute -2: -10x + 2 = -38, then subtract 2 from both sides: -10x = -40, and finally divide by -10: x = 4.

Front

What is the solution to the equation 10 - 5x + 20 = 50?

Back

Combine like terms to get 30 - 5x = 50, then isolate x: -5x = 20, so x = -4.

Front

How do you solve the equation 8x + 6 = 4x - 14?

Back

Subtract 4x from both sides: 4x + 6 = -14, then subtract 6: 4x = -20, and divide by 4: x = -5.

Front

What is the solution to the equation 3x = -2x + 5 + 10x?

Back

Combine like terms: 3x = 8x + 5, then subtract 8x from both sides: -5x = 5, so x = -1.

Front

What does it mean to isolate a variable in an equation?

Back

To isolate a variable means to manipulate the equation so that the variable is on one side by itself.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What is the solution of an equation?

Back

The solution of an equation is the value of the variable that makes the equation true.

Front

What does it mean to combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.