Chapter 8.2, Problem 72HP

To determine

His mistake and correct it

Answer to Problem 72HP

The solution of the given equation is $x=29$

His mistake is that he add 7 both sides

Explanation of Solution

Given:

Toshiro is solving the equation $7-2x=-51$

  

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $7-2x=-51$ for the variable, isolate the variable term x on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate x on right side, first subtract both sides by $7$ and then divide both sides by $2$ and then simplify further as shown below,

  $\begin{array}{c}7-2x=-51\\ 7-2x-7=-51-7\\ -2x=-58\\ \frac{-2x}{-2}=\frac{-58}{-2}\\ x=29\end{array}$

Thus, the solution of the given equation is $x=29$

His mistake is that he add 7 both sides