Solving Two-Step Equations with Inverses

This tutorial teaches how to solve equations using two inverse steps. It begins with identifying the variable and determining which side of the equation to work with. The tutorial explains how to clear fractions by multiplying by the denominator and using inverse operations to eliminate constants and coefficients. Several examples are provided to illustrate these steps, including handling fractions and coefficients in different positions. The lesson concludes with a summary of the techniques covered.

What is the first step in solving equations using two inverse steps?

• Identify the variable

• Use a calculator

• Clear the constants

• Multiply by the denominator

If the variable is in the numerator of a fraction, what should you do?

• Multiply every term by the denominator

• Subtract the denominator from both sides

• Divide every term by the denominator

• Add the denominator to both sides

What is the purpose of using inverse operations in solving equations?

• To add more variables

• To change the equation's sides

• To make the equation more complex

• To clear the constants and coefficients

In the example 6x + 4 = -32, which number is easier to clear first?

• 6

• 4

• 32

• None of the above

What do additive inverses do in an equation?

• Double the value

• Make a one

• Make a zero

• Halve the value

What is the result of dividing a number by its multiplicative inverse?

• The same number

• Negative one

• One

• Zero

When the coefficient is in the denominator, what is the opposite operation of dividing?

• Subtracting

• Adding

• Multiplying

• Dividing

What should you do if you need to clear a fraction in an equation?

• Add the numerator

• Subtract the numerator

• Multiply by the reciprocal

• Divide by the reciprocal

In the final example, what does the negative sign belong to?

• The equation

• The variable

• The coefficient

• The constant

What is the final step in solving an equation with a fractional coefficient?

• Divide by the reciprocal

• Add the reciprocal

• Subtract the reciprocal

• Multiply by the reciprocal