Multistep Equations - Variables on Both Sides

Front

What is a multistep equation?

Back

A multistep equation is an equation that requires more than one step to solve for the variable. It often involves combining like terms, using the distributive property, and isolating the variable.

Front

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

Back

Having variables on both sides of an equation means that the variable appears in more than one term across the equal sign, requiring manipulation to isolate the variable.

Front

How do you solve the equation 3x - x + 4 = 4(2x - 1)?

Back

Front

What is the solution to the equation 3(x - 1) = 2x + 9?

Back

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, often resulting from equivalent expressions on both sides.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there is no value for the variable that can satisfy the equation, often resulting from contradictory statements.

Front

How do you determine if an equation has infinite solutions or no solution?

Back

To determine this, simplify the equation. If you end up with a true statement (like 0 = 0), it has infinite solutions. If you get a false statement (like 0 = 5), it has no solution.

Front

Solve the equation -2(x + 1) = -2x + 5.

Back

This equation has no solution because simplifying leads to a false statement.

Front

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

Back

The solution is infinite solutions, as both sides simplify to the same expression.

Front

How do you simplify the equation 2x - x + 7 = x + 3 + 4?

Back

Combine like terms to get x + 7 = x + 7, which leads to infinite solutions.