Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that has variables on both the left and right sides, requiring manipulation to isolate the variable.

Front

How do you solve the equation 6z = 49 - z?

Back

Add z to both sides to get 7z = 49, then divide by 7 to find z = 7.

Front

What is the first step to solve -49 - x = -8x + 70?

Back

Add x to both sides to combine like terms, resulting in -49 = -7x + 70.

Front

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

Back

To manipulate the equation so that the variable is alone on one side, making it easy to find its value.

Front

Solve for x: 5x - 14 = 8x + 4.

Back

Subtract 5x from both sides to get -14 = 3x + 4, then subtract 4 to find x = -6.

Front

What is the solution to the equation 14p - 8 = 22 + 20p?

Back

Subtract 14p from both sides to get -8 = 6p + 22, then solve for p to find p = -5.

Front

How do you check if your solution for an equation is correct?

Back

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

Front

What is the solution for f in the equation f - 4 = 6f + 26?

Back

Subtract f from both sides to get -4 = 5f + 26, then solve for f to find f = -6.

Front

What is a variable in an equation?

Back

A symbol, often a letter, that represents an unknown value in mathematical expressions.

Front

What does it mean to combine like terms in an equation?

Back

To simplify an expression by adding or subtracting terms that have the same variable raised to the same power.