Q. 22

Question

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$\frac{2 x + 1}{3} + 16 = 3 x$

Step-by-Step Solution

Verified

Answer

The required solution is $x = 7$ . The graph of the solution is given below:

1Step 1. Given information.

We have:

$\frac{2 x + 1}{3} + 16 = 3 x$

2Step 2. Solve the equation algebraically.

The equation is $\frac{2 x + 1}{3} + 16 = 3 x$ .

Substract $16$ from both sides:

$\frac{2 x + 1}{3} + 16 - 16 = 3 x - 16 \frac{2 x + 1}{3} = 3 x - 16$

Multiply both sides by $3 :$

$\frac{2 x + 1}{3} \cdot 3 = 3 x \cdot 3 - 16 \cdot 3 2 x + 1 = 9 x - 48 2 x + 1 - 1 = 9 x - 48 - 1 2 x = 9 x - 49 2 x - 9 x = 9 x - 49 - 9 x - 7 x = - 49 \frac{- 7 x}{- 7} = \frac{- 49}{- 7} x = 7$

3Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x = 7 .$

Draw the graph of the equation $\frac{2 x + 1}{3} + 16 = 3 x$ using the graphing utility:

Q. 21

Q. 23

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