Solving equations

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What is the first step in solving the equation 3(x - 2) = 18?

Back

Distribute the 3 to both terms inside the parentheses: 3x - 6 = 18.

Front

How do you isolate the variable in the equation 3x - 6 = 18?

Back

Add 6 to both sides to get 3x = 24, then divide by 3 to find x = 8.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no variables raised to a power greater than one.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can satisfy the equation.

Front

What does it mean if an equation has infinitely many solutions?

Back

An equation has infinitely many solutions if any value of the variable satisfies the equation.

Front

How do you solve the equation 3 + (1/4)a = 31?

Back

Subtract 3 from both sides to get (1/4)a = 28, then multiply both sides by 4 to find a = 112.

Front

What is the solution to the equation r/4 - 12 = -5?

Back

Add 12 to both sides to get r/4 = 7, then multiply both sides by 4 to find r = 28.

Front

What is the solution to the equation 11 = x - 7?

Back

Add 7 to both sides to find x = 18.