Solving Equations with Variables on Both Sides - H

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What are variables in an equation?

Back

Variables are symbols (like x or y) that represent unknown values in an equation.

Front

What does it mean to have variables on both sides of an equation?

Back

It means that the variable appears in expressions on both sides of the equality sign.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform operations to get the variable alone on one side of the equation.

Front

What is the first step in solving the equation 5x - 14 = 8x + 4?

Back

The first step is to move all terms involving x to one side and constant terms to the other side.

Front

What is the solution to the equation 5x - 14 = 8x + 4?

Back

The solution is x = -6.

Front

How do you check if your solution is correct?

Back

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

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 parenthesis.

Front

How do you apply the distributive property in the equation 4(1 - x) + 3x = -2(x + 1)?

Back

You distribute 4 to both 1 and -x, resulting in 4 - 4x + 3x = -2x - 2.