Solving Linear Equations Steps

This video tutorial provides guidance on solving equations, focusing on cases with no solution, infinite solutions, and one solution. The instructor demonstrates two examples: one resulting in infinite solutions and another with no solution. Key steps include distributing terms, combining like terms, and isolating variables. The video concludes with tips for simplifying equations and encourages viewers to ask questions if needed.

What are the three types of solutions that can occur when solving equations?

• One solution, two solutions, and three solutions

• No solution, one solution, and two solutions

• No solution, infinite solutions, and one solution

• Infinite solutions, two solutions, and three solutions

In the equation 4(X + 3) - 4 = 8(1/2X + 1), what is the first step to solve it?

• Add 4 to both sides

• Distribute the 4 and 8

• Combine like terms

• Subtract 8 from both sides

After distributing in the equation 4(X + 3) - 4 = 8(1/2X + 1), what is the next step?

• Subtract 4X from both sides

• Add 4 to both sides

• Multiply both sides by 2

• Combine like terms on both sides

What conclusion can be drawn if both sides of an equation simplify to the same value?

• The equation is invalid

• There are infinite solutions

• There is one solution

• There is no solution

In the equation X + 5X + 4 = 3(2X - 1), what is the first step to solve it?

• Combine like terms on the left side

• Distribute the 3 on the right side

• Subtract 4 from both sides

• Add 1 to both sides

What does it mean if an equation simplifies to a false statement like 4 = -3?

• There is one solution

• There are infinite solutions

• There is no solution

• The equation is incorrect

What should you do after distributing terms in an equation?

• Multiply both sides by 2

• Subtract the smallest term

• Combine like terms on each side

• Add all terms together

What is a key step in solving equations after combining like terms?

• Add the constant to both sides

• Multiply by the reciprocal

• Divide by the coefficient of X

• Isolate the variable on one side

Why is it important to get variables on one side of the equation?

• To eliminate fractions

• To ensure the equation is balanced

• To easily identify the solution

• To make the equation look simpler

What should you remember to do when solving equations?

• Simplify like terms and isolate variables

• Always add 1 to both sides

• Subtract the largest term

• Multiply all terms by 2