Algebra Examples

$\frac{z}{4} + 22 \leq 38$

Step 1

Move all terms not containing $z$ to the right side of the inequality.

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Step 1.1

Subtract $22$ from both sides of the inequality.

$\frac{z}{4} \leq 38 - 22$

Step 1.2

Subtract $22$ from $38$ .

$\frac{z}{4} \leq 16$

Step 2

Multiply both sides by $4$ .

$\frac{z}{4} \cdot 4 \leq 16 \cdot 4$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{z}{4} \cdot 4 \leq 16 \cdot 4$

Step 3.1.1.2

Rewrite the expression.

$z \leq 16 \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $16$ by $4$ .

$z \leq 64$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$z \leq 64$

Interval Notation:

$(- \infty, 64]$