Two-Step Equations

Front

What is a two-step equation?

Back

A two-step equation is an algebraic equation that requires two operations to solve for the variable. Typically, it involves isolating the variable by performing an inverse operation twice.

Front

How do you isolate a variable in a two-step equation?

Back

To isolate a variable in a two-step equation, perform the inverse operations in reverse order: first, eliminate any addition or subtraction, and then eliminate any multiplication or division.

Front

What is the first step to solve the equation \( \frac{v-3.8}{2}=-0.45 \)?

Back

Multiply both sides of the equation by 2 to eliminate the fraction.

Front

What is the solution to the equation \( 116.4=12(k+7.1) \)?

Back

The solution is \( k = 2.6 \). First, divide both sides by 12, then subtract 7.1.

Front

How do you convert a mixed number to an improper fraction?

Back

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.

Front

What is the solution to the equation \( 1\frac{2}{3}(5\frac{2}{5}+x)=\frac{13}{2} \)?

Back

The solutions are \( x = -\frac{3}{2} \) or \( x = -1.5 \). First, convert mixed numbers to improper fractions and then isolate x.

Front

What does it mean to distribute in an equation?

Back

Distributing means multiplying a term outside of parentheses by each term inside the parentheses.

Front

What is the solution to the equation \( -20.1(b-30)=791.94 \)?

Back

The solution is \( b = -9.4 \). First, divide both sides by -20.1 and then add 30.

Front

How do you check your solution for a two-step equation?

Back

To check your solution, substitute the value back into the original equation to see if both sides are equal.

Front

What is the solution to the equation \( 683.12=-25-12.6v \)?

Back

The solution is \( v = -56.2 \). First, add 25 to both sides, then divide by -12.6.