Equations with variables on both sides

Front

What is an equation with variables on both sides?

Back

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

Front

How do you solve the equation 28 + 3r = 10r?

Back

Subtract 3r from both sides: 28 = 10r - 3r; then, 28 = 7r; divide by 7: r = 4.

Front

What is the first step in solving 5y + 34 = -2(-7y + 1)?

Back

Distribute -2 to both terms inside the parentheses: 5y + 34 = 14y - 2.

Front

How do you isolate y in the equation 5y + 34 = 14y - 2?

Back

Subtract 5y from both sides: 34 = 9y - 2; then add 2: 36 = 9y; divide by 9: y = 4.

Front

What is the solution to the equation 7x = 3x + 24?

Back

Subtract 3x from both sides: 4x = 24; divide by 4: x = 6.

Front

How do you solve the equation 7(p + 9) = -21?

Back

First, divide both sides by 7: p + 9 = -3; then subtract 9: p = -12.

Front

What is the solution to the equation 2x = x + 3?

Back

Subtract x from both sides: x = 3.

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

What is the importance of checking your solution in an equation?

Back

To verify that the solution satisfies the original equation, ensuring accuracy.

Front

What is the general strategy for solving equations with variables on both sides?

Back

Combine like terms, isolate the variable, and simplify the equation step by step.