Solving Equations with Variables on Both Sides

Mr. Richards teaches how to solve equations with variables on both sides through various examples. The lesson covers moving variables to one side, checking solutions, and applying these techniques to real-world problems. Examples include working with positive numbers, using common denominators, and handling fractions. The video emphasizes understanding the process and verifying solutions.

What is the first step in solving the equation 8a = 5a + 21?

• Multiply both sides by 5

• Subtract 5a from both sides

• Add 5a to both sides

• Divide both sides by 8

After moving the variable terms to one side in the equation 8a = 5a + 21, what is the resulting equation?

• 13a = 21

• 3a = 21

• 5a = 21

• 8a = 26a

In Example B, why does the teacher prefer to subtract 3x from both sides instead of 8x?

• To work with smaller numbers

• To work with positive numbers

• To make the equation simpler

• To avoid fractions

What is the solution to the equation 3x - 7 = 8x + 23 after isolating the variable?

• x = -6

• x = 5

• x = -5

• x = 6

In Example C, what is the equation for the perimeter of the flag in terms of its width?

• P = 2L + 2W

• P = W + 14.4

• P = 2(2W - 0.3) + 2W

• P = 2W + 14.4

What is the width of the flag if the perimeter is 14.4 feet longer than the width?

• W = 2 feet

• W = 3 feet

• W = 4 feet

• W = 5 feet

In Example E, what is the common denominator used to solve the equation 12p + 7 = 34p + 9?

• 3

• 8

• 4

• 2

What is the solution to the equation 12p + 7 = 34p + 9 after isolating the variable?

• p = 4

• p = 8

• p = 2

• p = 1

In Example F, what is the first step in solving the equation -54c - 12 = -34 + 58c?

• Add 12 to both sides

• Subtract 58c from both sides

• Subtract 108c from both sides

• Add 108c to both sides

What is the final solution to the equation -54c - 12 = -34 + 58c?

• c = 2/15

• c = 1/2

• c = 3/4

• c = 4/5