To solve for \( x \), let's break down the compound inequality:
\( 2 \leq -2x - 2 \leq 8 \)
First, we will solve for \( x \) in both inequalities. Start by adding 2 to all three parts to isolate the term with \( x \) in the middle.
\( 2 + 2 \leq -2x - 2 + 2 \leq 8 + 2 \)
\( 4 \leq -2x \leq 10 \)
Next, we will divide all parts by -2 to solve for \( x \). Remember that when you divide or multiply by a negative number in an inequality, you have to reverse the direction of the inequality signs.
\( 4 / (-2) \geq x \geq 10 / (-2) \)
\( -2 \geq x \geq -5 \)
So, the solution is:
\( -5 \leq x \leq -2 \)
Now we'll graph this solution on a number line.
```
: -6 -5 -4 -3 -2 -1 0 1
Number line: ------|-----|-----|-----|-----|-----|-----|-----|--->
[ |=====|=====|=====| ]
```
The square brackets [ and ] suggest that the endpoints -5 and -2 are included in the solution.
On the number line, the section between -5 and -2 is filled in to represent all the numbers that satisfy the inequality, including -5 and -2 themselves.
Solve for xx and graph the solution on the number line below.
2, is less than or equal to, minus, 2, x, minus, 2, is less than or equal to, 8
2≤−2x−2≤
8
1 answer