Trigonometry Examples

$4 k - 6 < 3 k + k - 1$

Step 1

Rewrite so $k$ is on the left side of the inequality.

$3 k + k - 1 > 4 k - 6$

Step 2

Add $3 k$ and $k$ .

$4 k - 1 > 4 k - 6$

Step 3

Move all terms containing $k$ to the left side of the inequality.

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Step 3.1

Subtract $4 k$ from both sides of the inequality.

$4 k - 1 - 4 k > - 6$

Step 3.2

Combine the opposite terms in $4 k - 1 - 4 k$ .

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Step 3.2.1

Subtract $4 k$ from $4 k$ .

$0 - 1 > - 6$

Step 3.2.2

Subtract $1$ from $0$ .

$- 1 > - 6$

Step 4

Since $- 1 > - 6$ , the inequality will always be true for any value of $k$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$