Question

Solve the inequality and write your answer in interval notation.
-10≤-4x+6<2
-5,
-4,
-3,
-2,
-1
0
1
2
3
4
5
Interval notation for the above graph and inequality is

Answer 1

To solve the compound inequality \(-10 \leq -4x + 6 < 2\), we will break this into two parts and solve each one separately.

1. **Solving \(-10 \leq -4x + 6\)**:

\[
-10 \leq -4x + 6
\]

Subtract 6 from both sides:

\[
-16 \leq -4x
\]

Divide both sides by \(-4\), and remember to reverse the inequality:

\[
4 \geq x \quad \text{or} \quad x \leq 4
\]

2. **Solving \(-4x + 6 < 2\)**:

\[
-4x + 6 < 2
\]

Subtract 6 from both sides:

\[
-4x < -4
\]

Divide both sides by \(-4\), again remembering to reverse the inequality:

\[
x > 1
\]

Now we have the two inequalities from the compound inequality:
\[
1 < x \leq 4
\]

This means \(x\) is greater than 1 and less than or equal to 4.

In interval notation, this solution is represented as:
\[
(1, 4]
\]

**Final Answer:**
The interval notation for the solution is \((1, 4]\).