Variables on Both Sides

Front

What is a variable in an equation?

Back

A symbol used to represent an unknown value in mathematical expressions or equations.

Front

What does it mean to solve an equation with variables on both sides?

Back

It involves isolating the variable by moving terms containing the variable to one side and constant terms to the other side.

Front

What is the first step in solving the equation 7x − 2(x + 12) = −5 − 2(1 − 3x)?

Back

Distribute the -2 on the left side and -2 on the right side.

Front

How do you combine like terms in an equation?

Back

Add or subtract coefficients of the same variable or constant terms.

Front

What is the solution to the equation 4 − 7(v − 9) = −7 − 6(v − 10)?

Back

v = 14.

Front

What does it mean if an equation has no solution?

Back

It means that there is no value for the variable that can satisfy the equation.

Front

What is the significance of the distributive property in solving equations?

Back

It allows you to multiply a single term by terms inside parentheses, simplifying the equation.

Front

What is the solution to the equation −3(10 + 4v) = −6(5 − 9v)?

Back

v = 0.

Front

What is the purpose of isolating the variable in an equation?

Back

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

Front

What is the solution to the equation 11(b + 2) = 11(−10 + 3b)?

Back

b = 6.