HA: 10. multi-step equations and word problem FLASHCARD

Front

What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, and division.

Front

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

Back

First, distribute the 2: 3x + 8x - 8 = 3. Then combine like terms: 11x - 8 = 3. Add 8 to both sides: 11x = 11. Finally, divide by 11: x = 1.

Front

What is the first step in solving the equation 85 = 5(2x - 5) + x?

Back

The first step is to distribute the 5: 85 = 10x - 25 + x.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values that can satisfy the equation, often resulting in a contradiction.

Front

How do you find the smallest of three consecutive integers that sum to 87?

Back

Let the integers be x, x+1, and x+2. Set up the equation: x + (x+1) + (x+2) = 87. Solve for x to find the smallest integer.

Front

What is the solution to the equation 4(2x - 6) = 48?

Back

First, divide both sides by 4: 2x - 6 = 12. Then add 6 to both sides: 2x = 18. Finally, divide by 2: x = 9.

Front

What is a word problem in mathematics?

Back

A word problem is a mathematical problem that is presented in the form of a narrative or real-life scenario, requiring interpretation and problem-solving skills.

Front

How do you determine how many items you can buy with a given amount of money?

Back

To determine how many items you can buy, divide the total amount of money by the cost of one item.

Front

What is the process of combining like terms in an equation?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power to simplify the equation.

Front

What is the significance of the distributive property in solving equations?

Back

The distributive property allows you to multiply a single term by each term inside a set of parentheses, which is essential for simplifying expressions.