solving multi-step equations

Front

What is a multi-step equation?

Back

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

Front

How do you solve the equation 2x - 3 + 4x = 27?

Back

Combine like terms: 6x - 3 = 27. Then add 3 to both sides: 6x = 30. Finally, divide by 6: x = 5.

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 makes the equation true, often resulting in a contradiction.

Front

What is the solution to the equation 3x + 15 = 3(x + 5)?

Back

The equation simplifies to 3x + 15 = 3x + 15, which is true for all values of x, meaning the solution is all real numbers (infinite).

Front

How do you determine if an equation has infinite solutions?

Back

An equation has infinite solutions when both sides simplify to the same expression, indicating that any value for the variable will satisfy the equation.

Front

Solve the equation 2x + 1 = 2(x - 10). What is the solution?

Back

The equation simplifies to 2x + 1 = 2x - 20. Subtracting 2x from both sides gives 1 = -20, which is a contradiction, so there is no solution.

Front

What is the first step in solving the equation 38 + 7k = 8(k + 4)?

Back

Distribute the 8 on the right side: 38 + 7k = 8k + 32.

Front

How do you isolate the variable in the equation 38 + 7k = 8k + 32?

Back

Subtract 7k from both sides: 38 = k + 32. Then subtract 32 from both sides: k = 6.

Front

What is the solution to the equation 2x + 3(5x - 7) = 47?

Back

Distributing gives 2x + 15x - 21 = 47. Combine like terms: 17x - 21 = 47. Add 21 to both sides: 17x = 68. Finally, divide by 17: x = 4.

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 each term inside a parenthesis.