Chapter 8.2, Problem 64IP

To determine

The solution of the equation $\frac{3x}{2}+4x=22$ and check.

Answer to Problem 64IP

  $x=4$

Explanation of Solution

Given:

The equation, $\frac{3x}{2}+4x=22$

Concept Used:

• Least Common Denominator (LCD) is the smallest number that is divisible by the denominator of all the fractions that are being added or subtracted.
• Solving an equation containing rational expressions
1. Multiply both sides of equations by LCD(least common denominator) of all denominators.
2. Remove any grouping symbols and solve the resulting equation for the variable asked in equation

Calculation:

In order to solve the given equation, multiply both sides by 2 to get rid of the denominator in the first term and then simplify further by combining the like and perform algebraic operations as shown below

  $\begin{array}{c}\frac{3x}{2}+4x=22\\ \left(\frac{3x}{2}+4x\right)\cdot 2=22\cdot 2\\ \frac{3x}{2}\cdot 2+4x\cdot 2=44\\ 3x+8x=44\\ 11x=44\\ \frac{11x}{11}=\frac{44}{11}\\ x=4\end{array}$

Thus, the solution to the given equation is $x=4$ .

Now to check the solution, substitute $x=4$ in the given equation and check whether the left hand side and right hand side are coming out equal or no. So, it gives

  $\begin{array}{c}\frac{3\cdot 4}{2}+4\cdot 4=22\\ \frac{12}{2}+16=22\\ 6+16=22\end{array}$

    $\begin{array}{c}22=22\text{\hspace{1em}\hspace{1em}\hspace{1em}True statement}\end{array}$

Thus, the solution is correct.