Solving Linear Equations with Rational Coefficients

Front

What is the goal when solving a linear equation?

Back

To isolate the variable on one side of the equation and the constants on the other side.

Front

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

Back

It means to add or subtract terms that have the same variable raised to the same power.

Front

What is the first step in solving the equation 3x + 6 = 10 + 3x + 4x?

Back

Combine like terms 3x and 4x on the same side of the equation.

Front

What is the first step in solving the equation 3n - 4 = -2 + 2n?

Back

Subtract 2n from both sides of the equation.

Front

What does it mean to distribute in an equation?

Back

To multiply each term inside a parenthesis by the term outside the parenthesis.

Front

What is the first step in solving the equation 2a - 4(a - 5) = 10?

Back

Distribute -4 to a and -5.

Front

What is the solution to the equation 3x + 2(4x - 4) = 3?

Back

x = 1.

Front

What is a rational coefficient in a linear equation?

Back

A coefficient that can be expressed as a fraction or ratio of two integers.

Front

What is the importance of keeping the equation balanced when solving?

Back

Any operation performed on one side must also be performed on the other side to maintain equality.

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.