Pre-Algebra Examples

$3 y - 5 < 2 (17 - 5 y)$

Step 1

Simplify $2 (17 - 5 y)$ .

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Step 1.1

Rewrite.

$3 y - 5 < 0 + 0 + 2 (17 - 5 y)$

Step 1.2

Simplify by adding zeros.

$3 y - 5 < 2 (17 - 5 y)$

Step 1.3

Apply the distributive property.

$3 y - 5 < 2 \cdot 17 + 2 (- 5 y)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2$ by $17$ .

$3 y - 5 < 34 + 2 (- 5 y)$

Step 1.4.2

Multiply $- 5$ by $2$ .

$3 y - 5 < 34 - 10 y$

Step 2

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

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Step 2.1

Add $10 y$ to both sides of the inequality.

$3 y - 5 + 10 y < 34$

Step 2.2

Add $3 y$ and $10 y$ .

$13 y - 5 < 34$

Step 3

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

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Step 3.1

Add $5$ to both sides of the inequality.

$13 y < 34 + 5$

Step 3.2

Add $34$ and $5$ .

$13 y < 39$

Step 4

Divide each term in $13 y < 39$ by $13$ and simplify.

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Step 4.1

Divide each term in $13 y < 39$ by $13$ .

$\frac{13 y}{13} < \frac{39}{13}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $13$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{13 y}{13} < \frac{39}{13}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y < \frac{39}{13}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $39$ by $13$ .

$y < 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$y < 3$

Interval Notation:

$(- \infty, 3)$