Answer :
To solve the inequality [tex]\(-8 \frac{1}{5} x + 3 \frac{1}{3} x \leq \frac{14}{15}\)[/tex], follow these steps:
1. Convert the mixed numbers to improper fractions:
- [tex]\(-8 \frac{1}{5}\)[/tex] becomes [tex]\(-8.2\)[/tex].
- [tex]\(3 \frac{1}{3}\)[/tex] becomes [tex]\(3.3333\)[/tex].
2. Combine the like terms:
- Add the coefficients of [tex]\(x\)[/tex]:
[tex]\[
-8.2 + 3.3333 = -4.8667
\][/tex]
3. Re-write the inequality with the combined coefficient:
[tex]\[
-4.8667x \leq \frac{14}{15}
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Divide both sides by [tex]\(-4.8667\)[/tex]. Remember, dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.
[tex]\[
x \geq \frac{14}{15} \div -4.8667 \approx -0.20896
\][/tex]
5. Conclusion:
The solution to the inequality is:
[tex]\[
x \geq -0.20896
\][/tex]
This result tells us that the value of [tex]\(x\)[/tex] must be greater than or equal to approximately [tex]\(-0.20896\)[/tex] to satisfy the inequality.
1. Convert the mixed numbers to improper fractions:
- [tex]\(-8 \frac{1}{5}\)[/tex] becomes [tex]\(-8.2\)[/tex].
- [tex]\(3 \frac{1}{3}\)[/tex] becomes [tex]\(3.3333\)[/tex].
2. Combine the like terms:
- Add the coefficients of [tex]\(x\)[/tex]:
[tex]\[
-8.2 + 3.3333 = -4.8667
\][/tex]
3. Re-write the inequality with the combined coefficient:
[tex]\[
-4.8667x \leq \frac{14}{15}
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Divide both sides by [tex]\(-4.8667\)[/tex]. Remember, dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.
[tex]\[
x \geq \frac{14}{15} \div -4.8667 \approx -0.20896
\][/tex]
5. Conclusion:
The solution to the inequality is:
[tex]\[
x \geq -0.20896
\][/tex]
This result tells us that the value of [tex]\(x\)[/tex] must be greater than or equal to approximately [tex]\(-0.20896\)[/tex] to satisfy the inequality.
