Question

6. Solve: 6x - 13 < 6(x - 2)
no solution

Answer 1

All real numbers are solutions.

Explanation:

Begin by expanding the right side (Distributive Property).

6x - 13 < 6x - 12

Notice that 6x appears on both sides, so when you try to get rid of 6x on the right by subtracting it, this happens:

-13 < -12

This is a true statement! Negative thirteen is less than negative twelve.

That's an indication that the original inequality is true for all real numbers.

If you had ended up with a false statement such as 4 > 13, that would indicate that no real numbers are solutions.

Answer 2

The Inequality is true for all real numbers.

Explanation:

We are given the Inequality:

`\displaystyle \large{6x - 13 < 6(x - 2)}`

First, expand 6 in.

`\displaystyle \large{6x - 13< 6x - 12}`

Subtract both sides by 6x.

`\displaystyle \large{6x - 13 - 6x< 6x - 12 - 6x} \\ \displaystyle \large{- 13< - 12 }`

Since variables no longer exist, there are two circumstances:

• The Inequality is false.
• The Inequality is true.

Since we know that -13 is less than -12, the Inequality is true for all real numbers.