Chapter 3: Q. 30 (page 151)

Solve the inequality. Graph your solution.
$- 3 \leq \frac{2 x + 4}{4}$

Short Answer

Expert verified

Solution of the inequality is $x \geq - 8$ .

Step by step solution

Step 1. Solve the inequality

$- 3 \leq \frac{2 x + 4}{4}$

Multiply both sides by 4.

$\begin{matrix} - 3 \times 4 \leq \frac{2 x + 4}{4} \times 4 \\ - 12 \leq 2 x + 4 \end{matrix}$

Subtract 4 on both sides.

$\begin{matrix} - 12 - 4 \leq 2 x + 4 - 4 \\ - 16 \leq 2 x \\ 2 x \geq - 16 \end{matrix}$

Divide both sides by 2.

$\begin{matrix} x \geq \frac{- 16}{2} \\ x \geq - 8 \end{matrix}$

Step 2. Graph the inequality

The solution of the inequality is $x \geq - 8$ .

That means, all values $x \geq - 8$ satisfy the inequality. So, the graph can be given as shown below.

Step 3. Check the solution

To check the solution, take any random number, $x \geq - 8$ and substitute in the original inequality and observe the result.

Take $x = 1$ .

Then,

$\begin{matrix} - 3 \leq \frac{2 \times 0 + 4}{4} \\ - 3 \leq \frac{0 + 4}{4} \\ - 3 \leq \frac{4}{4} \\ - 3 \leq 1 \end{matrix}$

The result $- 3 \leq 1$ is true. So, the solution \[x\ge -8\] is correct.

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Solve the inequality. Graph your solution.
$- 3 \leq \frac{2 x + 4}{4}$

Short Answer

Step by step solution

Step 1. Solve the inequality

Step 2. Graph the inequality

Step 3. Check the solution

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Solve the inequality. Graph your solution.-3≤2x+44

Short Answer

Step by step solution

Step 1. Solve the inequality

Step 2. Graph the inequality

Step 3. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Solve the inequality. Graph your solution.
$- 3 \leq \frac{2 x + 4}{4}$