Equations and Word Problems

Front

What is the first step to isolate the variable in the equation 20 = 2 - a?

Back

To isolate the variable a, you would subtract 2 from both sides, resulting in 18 = -a, and then multiply by -1 to get a = -18.

Front

How do you solve the equation x - 62 = 123?

Back

Add 62 to both sides of the equation to isolate x, resulting in x = 185.

Front

What is the solution to the equation x ÷ 2 = 12?

Back

Multiply both sides by 2 to isolate x, resulting in x = 24.

Front

What is the first step in solving the equation 2x + 1 = 6?

Back

Subtract 1 from both sides to isolate the term with x, resulting in 2x = 5.

Front

How do you calculate the total fare for a taxi ride that charges $3 plus $1.50 per mile?

Back

The total fare can be calculated using the formula: Total Fare = 3 + (1.50 * number of miles).

Front

If a taxi ride costs $30 and the base fare is $3, how do you find the number of miles traveled?

Back

First, subtract the base fare from the total fare: 30 - 3 = 27. Then, divide by the cost per mile: 27 ÷ 1.50 = 18 miles.

Front

What is the principle of balancing equations in algebra?

Back

The principle of balancing equations states that you can perform the same operation on both sides of an equation without changing its equality.

Front

What does it mean to isolate a variable in an equation?

Back

Isolating a variable means manipulating the equation so that the variable is on one side by itself, allowing you to solve for its value.

Front

What is the importance of showing work when solving equations?

Back

Showing work helps to track the steps taken to solve the equation, making it easier to identify errors and understand the solution process.

Front

What is a word problem in mathematics?

Back

A word problem is a mathematical question presented in a narrative form, requiring the translation of words into mathematical expressions or equations.