Chapter 3: Q .23CT (page 160)

Write the verbal sentence as an inequality. Also, solve the inequality
“Eight times the sum of $5$ and a number is less than $56$ .”

Short Answer

Expert verified

The equation is $8 (5 + x) < 56$ and the solution of inequality is $x < 2$ .

Step by step solution

Step 1. Apply the concept of linear inequalities

In this, simply use the concept of understanding the problem and their words very carefully and also take a suitable variable to make inequalities and also do various mathematical operation to get the solution.

Step 2. Find the inequality by explaining the statement

Here, The statement Eight times the sum of $5$ and a number is less than $56$ .

From the above, Let the number be x.

Then, according to statement of question, the inequality is $8 (5 + x) < 56$ .

Step 3. Finding the solution of inequality for x

Now, The inequality is $8 (5 + x) < 56$ .

Simply open the bracket, subtract $40$ to both side of the inequality and then divide $8$ to both side

$\begin{array}{l} 8 (5 + x) < 56 \\ 40 + 8 x < 56 \\ 8 x + 40 - 40 < 56 - 40 \\ 8 x < 16 \\ \frac{8 x}{8} < \frac{16}{8} \\ x < 2 \end{array}$

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Write the verbal sentence as an inequality. Also, solve the inequality
“Eight times the sum of $5$ and a number is less than $56$ .”

Short Answer

Step by step solution

Step 1. Apply the concept of linear inequalities

Step 2. Find the inequality by explaining the statement

Step 3. Finding the solution of inequality for x

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Write the verbal sentence as an inequality. Also, solve the inequality“Eight times the sum of 5 and a number is less than 56.”

Short Answer

Step by step solution

Step 1. Apply the concept of linear inequalities

Step 2. Find the inequality by explaining the statement

Step 3. Finding the solution of inequality for x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Pure Maths

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Write the verbal sentence as an inequality. Also, solve the inequality
“Eight times the sum of $5$ and a number is less than $56$ .”