Chapter 1.9, Problem 51MR

To determine

Write an equation involving addition and demonstrate two ways to solve it.

Answer to Problem 51MR

  $3x+34=133$; $x=33$

Explanation of Solution

Given:

Write an equation involving addition and demonstrate two ways to solve it .

Concept Used:

Addition or Subtraction Property of Equality:

If $\text{a}\text{=}\text{b}$ , then $\text{a}\text{+}\text{c}\text{=}\text{b}\text{+}\text{c}$ or If $\text{a}\text{=}\text{b}$ , then $\text{a}-\text{c}\text{=}\text{b}-\text{c}$

The property that states that if you add or subtract the same number to both sides of an equation, the sides remain equal (i.e., the equation continues to be true.)

Transposition Method for Solving Linear Equations in One Variable

Sometimes the two sides of an equation contain both variable and constants. In such cases, we first simplify two sides in their simplest forms and then transpose terms containing variable on R.H.S. to L.H.S. and constant terms on L.H.S. to R.H.S.

By transposing a term from one side to another side, we mean changing its sign and carrying it to the other side. In transposition, the plus sign of the term changes into minus sign on the other side and vice −versa.

Calculation:

Let an equation is $3x+34=133$

We need to solve this equation in two ways.

In first way we can use the addition or subtraction property of equality.

Addition or Subtraction Property of Equality:

If $\text{a}\text{=}\text{b}$ , then $\text{a}\text{+}\text{c}\text{=}\text{b}\text{+}\text{c}$ or If $\text{a}\text{=}\text{b}$ , then $\text{a}-\text{c}\text{=}\text{b}-\text{c}$

The property that states that if you add or subtract the same number to both sides of an equation, the sides remain equal (i.e., the equation continues to be true.)

Steps	Explanation
$3x+34=133$	Original Equation
$3x+34-34=133-34$	Subtract 34 from each side.
$3x=99$	Simplify
$\frac{3x}{3}=\frac{99}{3}$	Divide each side by 3. Coefficient of x
$x=33$	Solution.
$\begin{array}{l}3x+34=133\\ 3·33+34=133\\ 99+34=133\\ 134=134\end{array}$	Check the solution. When $x=33$

In the second way we can use the transposition method.

Transposition Method: By transposing a term from one side to another side, we mean changing its sign and carrying it to the other side.

In transposition, the plus sign of the term changes into minus sign on the other side and vice −versa.

Steps	Explanation
$3x+34=133$
$3x=133-34$	Transpose 34 from left side To right side.
$3x=99$	Simplify
$\frac{3x}{3}=\frac{99}{3}$	Divide each side by 3. Coefficient of x
$x=33$	Solution
$\begin{array}{l}3x+34=133\\ 3·33+34=133\\ 99+34=133\\ 134=134\end{array}$	Check the solution. When $x=33$

Thus, the equation is $3x+34=133$ and solution $x=33$ , shown in two ways.