Question

- 6(x - 2) = 36 or 4 + x < 14 Step 3 of 4: Using your answers from the previous steps, solve the overall inequality problem and express your answer in interval notation. Use decimal form for numerical values.

Answer 1

Question:

Solution:

Consider the following inequalities system :

Inequality 1:

`-6(x-2)\text{ }\leq36`

or

Inequality 2:

`4+x<14`

Applying the distributive property in inequality 1, we obtain:

`-6x+12\text{ }\leq36`

this is equivalent to:

`-6x\text{ }\leq36-12\text{ = 24}`

that is:

`-6x\leq24`

this is equivalent to:

`6x\ge-24`

solving for x, we get:

`x\text{ }\ge-(24)/(6)\text{ = -4}`

that is:

`x\text{ }\ge\text{ -4}`

Then inequality 1 is equivalent to the following solution

`x\text{ }\ge\text{ -4}`

On the other hand, for inequality 2 solving for x, we get:

`x<14-4\text{ = 10}`

that is:

`x<10`

so that, the solution to the inequality system is

`x\text{ }\ge\text{ -4}`

or

`x<10`

now, this is equivalent to say:

`x\text{ }\ge\text{ -4 U x<10}`

or in interval notation:

`\lbrack-4,+\infty)\text{ U (-}\infty\text{,10) }`