The solutions of the related equation are approximately $- 1.58$ and $1.58 .$ Let's plot them on a number line. Since the original is not a strict inequality, the points will be closed.

Step $3$

Finally, we must test a value from each interval to see if it satisfies the original inequality. Let's choose a value from the first interval,

x \leq - 1.58 .

For simplicity, we will choose

x = - 2 .

2 x^{2} + 4 \geq 9

Substitute

$x = - 2$

2 (- 2)^{2} + 4 \geq ? 9

▼

Simplify left-hand side

CalcPow

Calculate power

2 (4) + 4 \geq ? 9

Multiply

8 + 4 \geq ? 9

AddTerms

Add terms

12 \geq 9 ✓

Since

x = - 2

produced a true statement, the interval

x \leq - 1.58

is a part of the solution. Similarly, we can test the other two intervals.

Interval	Test Value	Statement	Is It Part of the Solution?
$- 1.58 \leq x \leq 1.58$	$0$	$4 ≱ 9$ $\times$	No
$x \geq 1.58$	$2$	$12 \geq 9$ $✓$	Yes

We can now write the solution set and show it on a number line.

{x ∣ x \leq - 1.58 or x \geq 1.58} or (- \infty, - 1.58] \cup [1.58, \infty)

Step 1

Step 2

Step 3

Step $1$

Step $2$

Step $3$

$x = \frac{\pm 1 0}{2}$
$x = \frac{1 0}{2}$	$x = \frac{- 1 0}{2}$
$x \approx 1.58$	$x \approx - 1.58$

Exercise 39 Page 286

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