7.10 A reteach solving 2 step equations - word problems

Front

What is a two-step equation?

Back

A two-step equation is an algebraic equation that requires two operations to solve for the variable. For example, in the equation 2x + 3 = 7, you would first subtract 3 and then divide by 2 to find x.

Front

How do you isolate a variable in a two-step equation?

Back

To isolate a variable in a two-step equation, perform the inverse operations in reverse order. First, eliminate the constant term by adding or subtracting, then eliminate the coefficient by multiplying or dividing.

Front

What does the equation 7x + 35 = 63 represent in a word problem?

Back

This equation represents a scenario where a person charges a fixed amount ($35) plus a variable amount based on the number of hours worked (7x), resulting in a total bill of $63.

Front

How can you write an equation from a word problem?

Back

To write an equation from a word problem, identify the variables, constants, and relationships described in the problem, then translate them into mathematical expressions.

Front

What is the first step to solve the equation 7x + 35 = 63?

Back

The first step is to subtract 35 from both sides of the equation to isolate the term with the variable: 7x = 63 - 35.

Front

What is the solution to the equation x/2 + 16 = 36?

Back

To solve x/2 + 16 = 36, first subtract 16 from both sides to get x/2 = 20, then multiply both sides by 2 to find x = 40.

Front

What does the equation y = -25x + 120 represent?

Back

This equation represents a linear relationship where y decreases by 25 for every increase of 1 in x, starting from a maximum value of 120.

Front

How do you interpret the slope in the equation y = -25x + 120?

Back

The slope of -25 indicates that for every unit increase in x, y decreases by 25 units, showing a negative correlation.

Front

What is the meaning of the constant term in a linear equation?

Back

The constant term in a linear equation represents the y-intercept, which is the value of y when x is zero.

Front

How do you set up an equation for a situation where you have a total amount and a fixed cost?

Back

Set up the equation by combining the fixed cost with a variable representing the total cost, then equate it to the total amount available.