Chapter 2: Q319. (page 184)

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$4 k - (k - 2) \geq 7 k - 26$

Short Answer

Expert verified

$k \leq 7$

$(- \infty, 7]$

Step by step solution

Step 1. Given information.

The given inequality is

$4 k - (k - 2) \geq 7 k - 26$

Step 2. Solving the inequality.

Distributing and combining like terms:

$4 k - k + 2 \geq 7 k - 26$

$3 k + 2 \geq 7 k - 26$

Subtracting $7 k + 2$ from both sides

$3 k + 2 - (7 k + 2) \geq 7 k - 26 - (7 k + 2)$

$3 k + 2 - 7 k - 2 \geq 7 k - 26 - 7 k - 2$

Combining like terms and simplifying

$- 4 k \geq - 28$

Diving both sides by $- 4$ (this will reverse the inequality as the division is being performed by a negative quantity)

$\frac{- 4 k}{- 4} \leq \frac{- 28}{- 4}$

Simplifying, the solution to the given inequality becomes

$k \leq 7$

Step 3. Graphing the solution on the number line.

The graph of the solution on the number line is presented below:

Step 4. Writing the solution in interval notation.

In interval notation, the solution can be expressed as

$(- \infty, 7]$

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Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$4 k - (k - 2) \geq 7 k - 26$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving the inequality.

Step 3. Graphing the solution on the number line.

Step 4. Writing the solution in interval notation.

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Solve the inequality, graph the solution on the number line and write the solution in the interval notation.4k-k-2≥7k-26

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving the inequality.

Step 3. Graphing the solution on the number line.

Step 4. Writing the solution in interval notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$4 k - (k - 2) \geq 7 k - 26$