Answered

Find solutions to your problems with the expert advice available on IDNLearn.com. Discover reliable answers to your questions with our extensive database of expert knowledge.

Solve the inequality.

[tex]\[ 6x - 2 \leq 9 \text{ or } 4 + 3x \ \textgreater \ 15 \][/tex]

[tex]\[ x \leq \frac{?}{?} \text{ or } x \ \textgreater \ ? \][/tex]

Sagot :

GinnyAnsweridn
To solve the inequalities given:

1. [tex]\(6x - 2 \leq 9\)[/tex]
2. [tex]\(4 + 3x > 15\)[/tex]

we will address them step-by-step.

### Solving the first inequality:
[tex]\[ 6x - 2 \leq 9 \][/tex]

1. Add 2 to both sides:
[tex]\[ 6x - 2 + 2 \leq 9 + 2 \][/tex]
[tex]\[ 6x \leq 11 \][/tex]

2. Divide both sides by 6:
[tex]\[ x \leq \frac{11}{6} \][/tex]

So, the solution to the first inequality is:
[tex]\[ x \leq \frac{11}{6} \][/tex]

### Solving the second inequality:
[tex]\[ 4 + 3x > 15 \][/tex]

1. Subtract 4 from both sides:
[tex]\[ 4 + 3x - 4 > 15 - 4 \][/tex]
[tex]\[ 3x > 11 \][/tex]

2. Divide both sides by 3:
[tex]\[ x > \frac{11}{3} \][/tex]

So, the solution to the second inequality is:
[tex]\[ x > \frac{11}{3} \][/tex]

### Combining the solutions:
Since the inequality involves "or", the combined solution is either the solution of the first inequality or the solution of the second inequality. Thus, the complete solution is:

[tex]\[ x \leq \frac{11}{6} \text{ or } x > \frac{11}{3} \][/tex]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.