Solving Equations

Front

What is the formula for the total cost of hiring a mechanic who charges a flat fee and an hourly rate?

Back

y = 65x + 15, where y is the total cost, x is the number of hours, $15 is the flat fee, and $65 is the hourly rate.

Front

How do you solve the equation 4x + 3 = -5?

Back

x = -2.

Front

What equation models the cost of hiring Eddie's Electric, who charges $90 per hour plus a $50 traveling fee?

Back

y = 90x + 50, where y is the total cost, x is the number of hours.

Front

Back

x = 20.

Front

What is the solution to the equation 6(5x - 3) = 36?

Back

x = \frac{9}{5}.

Front

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

Back

To isolate a variable means to manipulate the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you check if a solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is the first step in solving the equation 2x + 5 = 15?

Back

Subtract 5 from both sides to isolate the term with x.