Algebra Examples

$z + 4 \geq 2 z$

Step 1

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

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Step 1.1

Subtract $2 z$ from both sides of the inequality.

$z + 4 - 2 z \geq 0$

Step 1.2

Subtract $2 z$ from $z$ .

$- z + 4 \geq 0$

Step 2

Subtract $4$ from both sides of the inequality.

$- z \geq - 4$

Step 3

Divide each term in $- z \geq - 4$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- z \geq - 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- z}{- 1} \leq \frac{- 4}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{z}{1} \leq \frac{- 4}{- 1}$

Step 3.2.2

Divide $z$ by $1$ .

$z \leq \frac{- 4}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 4$ by $- 1$ .

$z \leq 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$z \leq 4$

Interval Notation:

$(- \infty, 4]$