Chapter 1: Q. 21 (page 29)

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$\frac{x + 1}{3} + \frac{x + 2}{7} = 5$

Short Answer

Expert verified

The required solution is $x = \frac{46}{5}$ . The graph of the solution is given below:

Step by step solution

Step 1. Given information.

We have:

$\frac{x + 1}{3} + \frac{x + 2}{7} = 5$

Step 2. Solve the equation algebraically.

The equation is $\frac{x + 1}{3} + \frac{x + 2}{7} = 5$ .

Find the least common multiplier of $3, 7$ : $21$

Multiply by LCM (Least common multiple) to both sides of the equation.

$\frac{x + 1}{3} \cdot 21 + \frac{x + 2}{7} \cdot 21 = 5 \cdot 21 7 (x + 1) + 3 (x + 2) = 105 7 x + 7 + 3 x + 6 = 105 10 x + 13 = 105$

Subtract $13$ to both sides:

$10 x + 13 - 13 = 105 - 13 10 x = 92 \frac{10 x}{10} = \frac{92}{10} x = \frac{46}{5}$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x = \frac{46}{5}$ .

Draw the graph of the equation $\frac{x + 1}{3} + \frac{x + 2}{7} = 5$ using the graphing utility:

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In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$\frac{x + 1}{3} + \frac{x + 2}{7} = 5$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the equation algebraically.

Step 3. Verify the solution using a graphing utility.

One App. One Place for Learning.

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In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.x+13 +x+27=5

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the equation algebraically.

Step 3. Verify the solution using a graphing utility.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Geometry

Calculus

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$\frac{x + 1}{3} + \frac{x + 2}{7} = 5$