Algebra Examples

$\frac{9 z - 4}{5} \leq \frac{7 z + 2}{4}$

Step 1

Multiply both sides by $5$ .

$\frac{9 z - 4}{5} \cdot 5 \leq \frac{7 z + 2}{4} \cdot 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $5$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{9 z - 4}{5} \cdot 5 \leq \frac{7 z + 2}{4} \cdot 5$

Step 2.1.1.2

Rewrite the expression.

$9 z - 4 \leq \frac{7 z + 2}{4} \cdot 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{7 z + 2}{4} \cdot 5$ .

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Step 2.2.1.1

Combine $\frac{7 z + 2}{4}$ and $5$ .

$9 z - 4 \leq \frac{(7 z + 2) \cdot 5}{4}$

Step 2.2.1.2

Move $5$ to the left of $7 z + 2$ .

$9 z - 4 \leq \frac{5 (7 z + 2)}{4}$

Step 3

Solve for $z$ .

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Step 3.1

Multiply both sides by $4$ .

$(9 z - 4) \cdot 4 \leq \frac{5 (7 z + 2)}{4} \cdot 4$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $(9 z - 4) \cdot 4$ .

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Step 3.2.1.1.1

Apply the distributive property.

$9 z \cdot 4 - 4 \cdot 4 \leq \frac{5 (7 z + 2)}{4} \cdot 4$

Step 3.2.1.1.2

Multiply.

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Step 3.2.1.1.2.1

Multiply $4$ by $9$ .

$36 z - 4 \cdot 4 \leq \frac{5 (7 z + 2)}{4} \cdot 4$

Step 3.2.1.1.2.2

Multiply $- 4$ by $4$ .

$36 z - 16 \leq \frac{5 (7 z + 2)}{4} \cdot 4$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $\frac{5 (7 z + 2)}{4} \cdot 4$ .

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Step 3.2.2.1.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1.1

Cancel the common factor.

$36 z - 16 \leq \frac{5 (7 z + 2)}{4} \cdot 4$

Step 3.2.2.1.1.2

Rewrite the expression.

$36 z - 16 \leq 5 (7 z + 2)$

Step 3.2.2.1.2

Apply the distributive property.

$36 z - 16 \leq 5 (7 z) + 5 \cdot 2$

Step 3.2.2.1.3

Multiply.

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Step 3.2.2.1.3.1

Multiply $7$ by $5$ .

$36 z - 16 \leq 35 z + 5 \cdot 2$

Step 3.2.2.1.3.2

Multiply $5$ by $2$ .

$36 z - 16 \leq 35 z + 10$

Step 3.3

Solve for $z$ .

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Step 3.3.1

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

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Step 3.3.1.1

Subtract $35 z$ from both sides of the inequality.

$36 z - 16 - 35 z \leq 10$

Step 3.3.1.2

Subtract $35 z$ from $36 z$ .

$z - 16 \leq 10$

Step 3.3.2

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

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Step 3.3.2.1

Add $16$ to both sides of the inequality.

$z \leq 10 + 16$

Step 3.3.2.2

Add $10$ and $16$ .

$z \leq 26$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$z \leq 26$

Interval Notation:

$(- \infty, 26]$