Chapter 9, Problem 13CT

To determine

To solve the equation $9+x=13$ and tell algebraic property of equality used.

Answer to Problem 13CT

Solution of $9+x=13$ is $x=4$

Subtraction property of equality and symmetry property of equality in addition is used to solve given equation.

Explanation of Solution

Given information:

Given equation,

  $9+x=13$

Concept used:

Subtraction property of equality states

  $\begin{array}{l}\text{For all real numbers }x,y\text{ and }z\\ \text{if }x=y,\text{ then }x-z=y-z\end{array}$

Symmetry property of equality in addition

  $\begin{array}{l}\text{For all real numbers }x,y\\ x+y=y+x\end{array}$

Use Subtraction property of equality to solve the given equation

  $\begin{array}{l}9+x=13\\ x+9=13\text{ (using symmetry property of equality in addition)}\\ \text{Subtract 9 both sides }\\ x+9-9=13-9\\ x+0=4\\ x=4\end{array}$

Conclusion:

Solution of $9+x=13$ is $x=4$

Subtraction property of equality and symmetry property of equality in addition is used to solve given equation.