Solving Multi-Step Linear Equations

Maria, a mathematician, explains how to solve multi-step linear equations using the DCI method: Distribute, Combine, and Inverse operations. She demonstrates the process with an example equation, highlighting the importance of distributing terms, combining like terms, and using inverse operations to isolate the variable and solve the equation.

What does the acronym DCI stand for in solving multi-step linear equations?

• Divide, Combine, Integrate

• Distribute, Combine, Invert

• Distribute, Calculate, Invert

• Divide, Calculate, Integrate

In the equation 2x + 4 = 3 * (2x - 6), what is the first step according to the DCI method?

• Add 4 to both sides

• Combine like terms

• Use inverse operations

• Distribute the 3

After distributing, what is the expression on the right side of the equation?

• 6x - 8

• 6x - 18

• 2x - 6

• 3x - 6

Why can't the terms on the left side of the equation be combined?

• They are not like terms

• They are already combined

• They are both variables

• They are on different sides

What is the first inverse operation used to get the variable on one side?

• Multiply both sides by 2

• Divide both sides by 2

• Subtract 2x from both sides

• Add 2x to both sides

After subtracting 2x from both sides, what is the new equation?

• 4 = 4x - 18

• 4x = 4 - 18

• 2x = 4x - 18

• 4 = 2x - 18

What operation is used to eliminate the -18 on the right side of the equation?

• Subtract 18 from both sides

• Add 18 to both sides

• Multiply both sides by 18

• Divide both sides by 18

What is the result of adding 18 to both sides of the equation?

• 4 = 18x

• 22 = 4x

• 4 = 22x

• 22 = 2x

What is the final step to solve for x in the equation 22 = 4x?

• Multiply both sides by 4

• Divide both sides by 4

• Subtract 4 from both sides

• Add 4 to both sides

What is the final value of x in the equation?

• 4.5

• 5

• 5.5

• 6