Solving Equations and Inequalities

This video tutorial guides viewers through translating a word problem into a system of equations and solving it. The problem involves finding two numbers where their sum is -35, and one number is five less than twice the other. The tutorial defines variables, translates the problem into equations, and demonstrates solving the system step by step, resulting in the numbers -25 and -10.

What is the first step in translating a word problem into a system of equations?

• Define the variables

• Guess the numbers

• Ignore the problem

• Solve the equations immediately

If the sum of two numbers is -35, how can this be expressed as an equation?

• n / m = -35

• n * m = -35

• n + m = -35

• n - m = -35

Why is it important to define variables in a word problem?

• To clearly represent unknowns

• To avoid solving the problem

• To make the problem longer

• To confuse the solver

What does the equation n + m = -35 represent in the context of the problem?

• The sum of two numbers

• The division of two numbers

• The product of two numbers

• The difference of two numbers

What is the significance of the number -35 in the problem?

• It is the product of the numbers

• It is the sum of the numbers

• It is the difference of the numbers

• It is the quotient of the numbers

What does 'one number is five less than twice the other' translate to in an equation?

• n = 2m + 5

• n = 2m - 5

• n = m - 5

• n = 5 - 2m

What is the equation for 'one number is five less than twice the other'?

• n = 2m + 5

• n = 2m - 5

• n = m - 5

• n = m + 5

What is the purpose of substituting one equation into another?

• To make the problem more complex

• To eliminate one variable

• To add more variables

• To guess the solution

After substituting and simplifying, what is the next step in solving the system of equations?

• Check the solution

• Add more variables

• Multiply each side of the equation by a number

• Divide each side of the equation by a number

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

• A more complex equation

• A longer equation

• A simplified equation

• An incorrect equation