Question

Solve the given inequality. Describe the solution set using the set builder or interval notation. Then graph the solution set on a number line. 3(x-5)>6

Answer 1

Answer: THIRD OPTION.

Step-by-step explanation:

Given the following inequality:

$3(x-5)\geq 6$

You can follow these steps in order to solve it:

1. Apply Distributive property on the left side:

$3(x-5)\geq 6\\\\(3)(x)+(3)(-5)\geq 6\\\\3x-15\geq 6$

2. Add 15 to both sides of the inequality:

$3x-15+(15)\geq 6+(15)\\\\3x\geq 21$

3. Finally, divide both sides of the inequality by 3:

$\frac{3x}{3}\geq \frac{21}{3}\\\\x\geq 7$

 The symbol is $\geq$ means "Greater than or equal to", and indicates that 7 is  include in the solution.

Therefore, the solution can be expressed as:

$[7, \infty)$

Now you must mark this point with a closed dot on the number line and shade everything to the right.