Question

Solve the following inequalities.



10
x
<
35
10x<35



x
x





−
10
y
<
35
−10y<35



y
y





10
z
<
−
35
10z<−35



z
z

Answer 1

Let's solve each of the inequalities step-by-step.

1. **Inequality:** \(10x < 35\)

To isolate \(x\), we divide both sides by 10:
\[
x < \frac{35}{10}
\]
Simplifying the fraction:
\[
x < 3.5
\]

2. **Inequality:** \(-10y < 35\)

To isolate \(y\), we divide both sides by \(-10\). Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign:
\[
y > \frac{35}{-10}
\]
Simplifying the fraction:
\[
y > -3.5
\]

3. **Inequality:** \(10z < -35\)

To isolate \(z\), we divide both sides by 10:
\[
z < \frac{-35}{10}
\]
Simplifying the fraction:
\[
z < -3.5
\]

**Summary of Solutions:**
- \(x < 3.5\)
- \(y > -3.5\)
- \(z < -3.5\)