Chapter 2: Q54. (page 102)

Solve each equation. Check your solution. (Lesson 2-3)
$\frac{1}{2} z + 7 = 16 - \frac{3}{5} z$

Short Answer

Expert verified

The solution of the given equation is $z = \frac{90}{11}$ .

Step by step solution

Step 1. Write the given equation.

The given equation is “ $\frac{1}{2} z + 7 = 16 - \frac{3}{5} z$ ”.

Step 2. Solve the given equation.

Solving,

$\frac{1}{2} z + 7 = 16 - \frac{3}{5} z$ (Given equation)

$\frac{1}{2} z + 7 + \frac{3}{5} z = 16 - \frac{3}{5} z + \frac{3}{5} z$ (Add $\frac{3}{5} z$ to both sides)

$\frac{11}{10} z + 7 = 16$ (Simplify)

$\frac{11}{10} z + 7 - 7 = 16 - 7$ (Subtract 7 from both sides)

$\frac{11}{10} z = 9$

$\frac{11}{10} z \times \frac{10}{11} = 9 \times \frac{10}{11}$ (Multiply both sides by $\frac{10}{11}$ )

$z = \frac{90}{11}$ (Simplify)

So, $z = \frac{90}{11}$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $z = \frac{90}{11}$ in the given equation $\frac{1}{2} z + 7 = 16 - \frac{3}{5} z$ to get,

$\begin{array}{l} \frac{1}{2} (\frac{90}{11}) + 7 = 16 - \frac{3}{5} (\frac{90}{11}) \\ \frac{45}{11} + 7 = 16 - 3 (\frac{18}{11}) \\ \frac{45 + 77}{11} = 16 - \frac{54}{11} \\ \frac{122}{11} = \frac{176 - 54}{11} \\ \frac{122}{11} = \frac{122}{11} \end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.

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Solve each equation. Check your solution. (Lesson 2-3)
$\frac{1}{2} z + 7 = 16 - \frac{3}{5} z$

Short Answer

Step by step solution

Step 1. Write the given equation.

Step 2. Solve the given equation.

Step 3. Check the obtained solution.

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Solve each equation. Check your solution. (Lesson 2-3)12z+7=16−35z

Short Answer

Step by step solution

Step 1. Write the given equation.

Step 2. Solve the given equation.

Step 3. Check the obtained solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Logic and Functions

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Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solution. (Lesson 2-3)
$\frac{1}{2} z + 7 = 16 - \frac{3}{5} z$