Chapter 4.5, Problem 29WE

To determine

To simplify the equation

  $15=3\left(x-1\right)+2\left(4-x\right)$

Answer to Problem 29WE

  $x=10$

Explanation of Solution

Given:

  $15=3\left(x-1\right)+2\left(4-x\right)$

Concept Used:

• To simplify an expression first use distributive property to remove any grouping symbol, and then add/subtract like terms.
• Distributive property: $a\left(b\pm c\right)=ab\pm ac$
• If an expression contains more than one operations between its terms and brackets, first solve the terms inside brackets and then apply division followed by multiplication, addition and subtraction.

Calculation:

To simplify the equation

  $15=3\left(x-1\right)+2\left(4-x\right)$

First use distributive property to remove any grouping symbol as,

  $\begin{array}{l}15=3\left(x-1\right)+2\left(4-x\right)\\ \text{or }3\left(x-1\right)+2\left(4-x\right)=15\\ \Rightarrow 3\left(x\right)-3\left(1\right)+2\left(4\right)-2\left(x\right)=15\\ \Rightarrow 3x-3+8-2x=15\\ \Rightarrow 3x-2x+8-3=15\\ \Rightarrow x+5=15\end{array}$

Now, subtract both sides of the equation by $5$ as,

  $\begin{array}{l}x+5-5=15-5\\ \Rightarrow x=10\end{array}$

Thus, the simplified equation becomes

  $x=10$