Solving and Simplifying Equations

The video tutorial guides viewers through solving a complex linear equation involving the variable 'a'. It begins by introducing the problem and then demonstrates how to simplify the equation by distributing terms and combining like terms. The tutorial continues by isolating the variable to solve the equation, and finally, it verifies the solution to ensure accuracy. The process is broken down into manageable steps, making it easier to understand and follow.

What is the initial equation that needs to be solved?

• 1/2 * (5 + a) = a/2 + 5/2

• 3 * (5 + a) = a/2 + 5/2

• 1/2 * (3 * (5 + a) - 2) = a/2 + 5/2

• 3 * (5 + a) - 2 = a/2 + 5/2

What is the result of distributing the 3 in the expression 3 * (5 + a)?

• 3a + 5

• 15 + 3a

• 15a + 3

• 5 + 3a

What is the simplified form of the right-hand side of the equation after combining terms?

• a + 5/2

• a/2 + 5

• 5a + 2

• a + 5

What operation is performed to eliminate the fraction in the equation?

• Multiply both sides by 2

• Divide both sides by 2

• Add 2 to both sides

• Subtract 2 from both sides

After multiplying both sides by 2, what is the new equation?

• 3a + 13 = a + 5

• 3a + 15 = a + 5

• 3a + 13 = 5

• 3a + 15 = 5

What is the next step after simplifying the equation to 3a + 13 = a + 5?

• Multiply both sides by 3

• Subtract a from both sides

• Add a to both sides

• Divide both sides by 3

What is the value of 'a' after solving the equation?

• 4

• -4

• 0

• 8

What is the purpose of substituting a = -4 back into the original equation?

• To verify the solution

• To eliminate fractions

• To find a new solution

• To simplify the equation

What does the left-hand side of the equation simplify to when a = -4?

• 2

• 1/2

• 0

• 1

What does the right-hand side of the equation simplify to when a = -4?

• 1/2

• 0

• 2

• 1