Mistakes in Solving Equations

The video tutorial explores common mistakes in solving algebraic equations through examples involving Lisa, Jin, Marina, and Taylor. Lisa makes a mistake by dividing each side of an equation by different numbers, Jin miscalculates a subtraction, Marina correctly solves her equation, and Taylor takes a non-helpful step in solving an equation. The tutorial emphasizes the importance of performing the same operation on both sides of an equation and highlights common pitfalls in algebraic problem-solving.

What was Lisa's first mistake when solving the equation 42 = 6a?

• She multiplied both sides by 6.

• She divided each side by different values.

• She subtracted 6 from both sides.

• She added 6 to both sides.

Why is it incorrect to divide each side of an equation by different values?

• It results in a non-equivalent equation.

• It simplifies the equation too much.

• It makes the equation unsolvable.

• It changes the equation to an inequality.

What is a valid algebraic operation when solving equations?

• Doing different operations on each side.

• Doing the same operation on both sides.

• Changing the equation to an inequality.

• Ignoring one side of the equation.

What was Jin's calculation error when solving x + 4.7 = 11.2?

• He multiplied both sides by 4.7.

• He calculated 11.2 - 4.7 incorrectly.

• He added 4.7 instead of subtracting.

• He subtracted 4.7 from only one side.

What should Jin have calculated when subtracting 4.7 from 11.2?

• 5.5

• 6.5

• 8.5

• 7.5

What was the correct operation Marina performed to solve 1/6 = 2/3y?

• She added 2/3 to both sides.

• She divided both sides by 2/3.

• She subtracted 1/6 from both sides.

• She multiplied both sides by 3/2.

What is the reciprocal of 2/3 that Marina used?

• 2/3

• 3/2

• 3/1

• 1/3

What was Taylor's initial mistake when solving n - 2.7 = 6.7?

• He added 2.7 to both sides.

• He subtracted 2.7 from both sides.

• He multiplied both sides by 2.7.

• He divided both sides by 2.7.

What was the result of Taylor's incorrect operation?

• n = 9.4

• n - 5.4 = 4

• n + 5.4 = 4

• n = 4

What should Taylor have done to isolate n in the equation n - 2.7 = 6.7?

• Add 2.7 to both sides.

• Subtract 2.7 from both sides.

• Multiply both sides by 2.7.

• Divide both sides by 2.7.