Solving Equations with Variables on Both Sides

Front

What does it mean to have 'no solution' in an equation?

Back

It means that there are no values for the variable that can satisfy the equation, often resulting from contradictory statements.

Front

How do you isolate a variable in an equation with variables on both sides?

Back

You can isolate a variable by moving all terms involving that variable to one side of the equation and constant terms to the other side.

Front

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

Back

Subtract 11 from both sides to begin isolating the variable.

Front

What is the formula to find the total cost for producing 't' teddy bears if the fixed cost is $1500 and the variable cost per bear is $8?

Back

Total cost = 1500 + 8t.

Front

How do you set up an equation to find the break-even point for a company selling products?

Back

Set the total cost equal to the total revenue, where total revenue is the price per item multiplied by the number of items sold.

Front

What is the solution to the equation 5y + 34 = -2(-7y + 1)?

Back

The solution is y = 4.

Front

What is the process of solving the equation 5x - 14 = 8x + 4?

Back

First, move all terms involving x to one side and constant terms to the other side, then solve for x.

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 significance of the coefficients in an equation?

Back

Coefficients determine the rate of change of the variable and affect the slope of the line represented by the equation.

Front

How can you check if your solution to an equation is correct?

Back

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