Solving Multi-step Linear Equations

Front

What is a multi-step linear equation?

Back

A multi-step linear equation is an equation that requires more than one step to solve for the variable, often involving combining like terms and using inverse operations.

Front

What is the first step in solving the equation 5x - 4 + 2x = 3?

Back

Combine like terms: 5x + 2x - 4 = 3, which simplifies to 7x - 4 = 3.

Front

How do you isolate the variable in the equation 7x - 4 = 3?

Back

Add 4 to both sides to get 7x = 7, then divide by 7 to find x = 1.

Front

What does it mean to 'combine like terms'?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Front

Solve the equation 3x + 2(4x - 4) = 3.

Back

Distribute the 2: 3x + 8x - 8 = 3. Combine like terms: 11x - 8 = 3. Add 8 to both sides: 11x = 11. Divide by 11: x = 1.

Front

What is the purpose of using parentheses in equations?

Back

Parentheses indicate that the operations inside them should be performed first according to the order of operations.

Front

Solve the equation 8v - 4(v + 8) = 8.

Back

Distribute -4: 8v - 4v - 32 = 8. Combine like terms: 4v - 32 = 8. Add 32 to both sides: 4v = 40. Divide by 4: v = 10.

Front

What is the solution to the equation -11 + 3(b + 5) = 7?

Back

Distribute 3: -11 + 3b + 15 = 7. Combine like terms: 3b + 4 = 7. Subtract 4: 3b = 3. Divide by 3: b = 1.

Front

What is the goal of solving a one, two, or multi-step equation?

Back

The goal is to find the value of the variable.

Front

What does 'inverse operations' mean in solving equations?

Back

Inverse operations are operations that undo each other, such as addition and subtraction or multiplication and division.