Chapter 2: Q322. (page 184)

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$\frac{3}{4} b - \frac{1}{3} b < \frac{5}{12} b - \frac{1}{2}$

Short Answer

Expert verified

Contradiction

No solution

Step by step solution

Step 1. Given information.

The following inequality is given

$\frac{3}{4} b - \frac{1}{3} b < \frac{5}{12} b - \frac{1}{2}$

Step 2. Solving the inequality.

Multiplying both sides by LCM $(12)$ to remove the fractions

$12 \times \frac{3}{4} b - 12 \times \frac{1}{3} b < 12 \times \frac{5}{12} b - 12 \times \frac{1}{2}$

Simplify

$9 b - 4 b < 5 b - 6 5 b < 5 b - 6$

Subtracting $5 b$ from both sides

$5 b - 5 b < 5 b - 6 - 5 b 0 < - 6$

Since the given statement is false, the inequality is a contradiction and it has no solution.

Step 3. Graph the inequality on the number line.

Since the inequality does not have a solution, it is not possible to plot the inequality on the number line

Step 4. Writing the solution in the interval notation.

The inequality does not have a solution.

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Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$\frac{3}{4} b - \frac{1}{3} b < \frac{5}{12} b - \frac{1}{2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving the inequality.

Step 3. Graph the inequality on the number line.

Step 4. Writing the solution in the interval notation.

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Solve the inequality, graph the solution on the number line and write the solution in the interval notation.34b-13b<512b-12

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving the inequality.

Step 3. Graph the inequality on the number line.

Step 4. Writing the solution in the interval notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Calculus

Logic and Functions

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$\frac{3}{4} b - \frac{1}{3} b < \frac{5}{12} b - \frac{1}{2}$