Question

solve and graph. your numbers may be exact or rounded to the nearest tenth. -3 + |-4 + 4x| ≥ 4

Explanation:

Step1: Isolate the absolute - value expression

Add 3 to both sides of the inequality $-3+\vert - 4 + 4x\vert\geq4$.
$\vert - 4 + 4x\vert\geq4 + 3$
$\vert - 4 + 4x\vert\geq7$

Step2: Split into two inequalities

For $\vert a\vert\geq b$ ($b\geq0$), we have $a\geq b$ or $a\leq - b$. Here $a=-4 + 4x$ and $b = 7$.
First inequality: $-4 + 4x\geq7$
Add 4 to both sides: $4x\geq7 + 4$
$4x\geq11$
Divide both sides by 4: $x\geq\frac{11}{4}=2.75$

Second inequality: $-4 + 4x\leq - 7$
Add 4 to both sides: $4x\leq-7 + 4$
$4x\leq - 3$
Divide both sides by 4: $x\leq-\frac{3}{4}=-0.75$

Answer:

$x\leq - 0.8$ or $x\geq2.8$ (rounded to the nearest tenth)

To graph on a number - line:

• Draw a number line.
• Mark the points $x=-0.8$ and $x = 2.8$ with closed circles (because the inequality is $\geq$ and $\leq$).
• Shade the region to the left of $x=-0.8$ and to the right of $x = 2.8$.