(7 question) 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, often involving operations such as addition, subtraction, multiplication, and division.

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 expressions on both the left and right sides of the equation, requiring manipulation to isolate the variable.

Front

How do you solve the equation 4(2x + 1) = 5x + 3x + 9?

Back

First, simplify both sides: 8x + 4 = 8x + 9. Then, subtract 8x from both sides: 4 = 9, which is a contradiction. Therefore, there is no solution.

Front

What is the solution to the equation 12 + 2x - x = 9x + 6?

Back

Combine like terms: 12 + x = 9x + 6. Then, subtract x from both sides: 12 = 8x + 6. Subtract 6: 6 = 8x. Finally, divide by 8: x = \frac{3}{4}.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when the two sides cannot be made equal, often resulting in a false statement like 4 = 9.

Front

How do you determine if an equation has infinite solutions?

Back

An equation has infinite solutions if, after simplification, both sides of the equation are identical, such as 0 = 0.

Front

Solve the equation 3(x - 1) = 2x + 9.

Back

Distribute: 3x - 3 = 2x + 9. Subtract 2x from both sides: x - 3 = 9. Add 3: x = 12.

Front

What is the solution to the equation -2(x + 1) = -2x + 5?

Back

Distribute: -2x - 2 = -2x + 5. Add 2x to both sides: -2 = 5, which is a contradiction. Therefore, there is no solution.

Front

Solve the equation 2(x + 2) + 3x = 2(x + 1) + 1.

Back

Distribute: 2x + 4 + 3x = 2x + 2 + 1. Combine like terms: 5x + 4 = 2x + 3. Subtract 2x: 3x + 4 = 3. Subtract 4: 3x = -1. Divide by 3: x = -\frac{1}{3}.

Front

What is the first step in solving a multistep equation?

Back

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