Chapter 2: Q318. (page 184)

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$6 h - 4 (h - 1) \leq 7 h - 11$

Short Answer

Expert verified

$h \geq 3$

$[3, \infty)$

Step by step solution

Step 1. Given information.

The following inequality is given

$6 h - 4 (h - 1) \leq 7 h - 11$

Step 2. Solving the inequality.

Distributing and combining like terms

$6 h - 4 h + 4 \leq 7 h - 11 2 h + 4 \leq 7 h - 11$

Subtracting $7 h + 4$ from both sides and simplifying

$2 h + 4 - (7 h + 4) \leq 7 h - 11 - (7 h + 4) 2 h + 4 - 7 h - 4 \leq 7 h - 11 - 7 h - 4 - 5 h \leq - 15$

Dividing both sides by $- 5$ (this will reverse the inequality as the division is being performed by a negative quantity)

$\frac{- 5 h}{5} \geq \frac{- 15}{5} h \geq 3$

Step 3. Graphing the inequality on the number line.

The graph of the solution on the number line is shown below

Step 4. Writing the solution in the interval notation.

The solution in the interval notation can be expressed as $[3, \infty)$

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Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$6 h - 4 (h - 1) \leq 7 h - 11$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving the inequality.

Step 3. Graphing 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.6h-4h-1≤7h-11

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving the inequality.

Step 3. Graphing 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

Probability and Statistics

Statistics

Decision Maths

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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.
$6 h - 4 (h - 1) \leq 7 h - 11$