Question

-4(4+7x) greater or equal to -7x+5

Answer 1

To solve the inequality \(-4(4+7x) \geq -7x + 5\), follow these steps:

1. Distribute \(-4\) on the left side:
\[
-4 \cdot 4 - 4 \cdot 7x \geq -7x + 5
\]
\[
-16 - 28x \geq -7x + 5
\]

2. Now, we'll get all terms involving \(x\) on one side and the constant terms on the other side. First, add \(28x\) to both sides:
\[
-16 \geq -7x + 28x + 5
\]
\[
-16 \geq 21x + 5
\]

3. Next, subtract \(5\) from both sides:
\[
-16 - 5 \geq 21x
\]
\[
-21 \geq 21x
\]

4. Finally, divide both sides by \(21\):
\[
\frac{-21}{21} \geq x
\]
\[
-1 \geq x \quad \text{or} \quad x \leq -1
\]

Thus, the solution to the inequality is:
\[
x \leq -1
\]

In interval notation, this can be expressed as:
\[
(-\infty, -1]
\]