1.3 Solving Equations with Variables on Both Sides

Front

What is the first step to solve the equation: 11 - 3x = 44?

Back

Subtract 11 from both sides.

Front

Solve for f: f - 4 = 6f + 26

Back

f = -6

Front

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.

Back

2 hours

Front

Solve the equation: 10x + 9 = 4x - 9

Back

x = -3

Front

What is the solution to the equation: x + 2 = x + 4?

Back

no solution

Front

What does it mean to have variables on both sides of an equation?

Back

It means that the variable appears on both sides of the equation, requiring manipulation to isolate the variable.

Front

What is the goal when solving an equation?

Back

To find the value of the variable that makes the equation true.

Front

What is the principle of balancing equations?

Back

Whatever you do to one side of the equation, you must do to the other side to maintain equality.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to move other terms to the opposite side.

Front

What is an example of an equation with no solution?

Back

x + 2 = x + 4.