Algebra Examples

$5 (7 - 3 x) > 6 (5 - 4 x)$

Step 1

Simplify $5 (7 - 3 x)$ .

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Step 1.1

Rewrite.

$0 + 0 + 5 (7 - 3 x) > 6 (5 - 4 x)$

Step 1.2

Simplify by adding zeros.

$5 (7 - 3 x) > 6 (5 - 4 x)$

Step 1.3

Apply the distributive property.

$5 \cdot 7 + 5 (- 3 x) > 6 (5 - 4 x)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $5$ by $7$ .

$35 + 5 (- 3 x) > 6 (5 - 4 x)$

Step 1.4.2

Multiply $- 3$ by $5$ .

$35 - 15 x > 6 (5 - 4 x)$

Step 2

Simplify $6 (5 - 4 x)$ .

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Step 2.1

Apply the distributive property.

$35 - 15 x > 6 \cdot 5 + 6 (- 4 x)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $6$ by $5$ .

$35 - 15 x > 30 + 6 (- 4 x)$

Step 2.2.2

Multiply $- 4$ by $6$ .

$35 - 15 x > 30 - 24 x$

Step 3

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

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Step 3.1

Add $24 x$ to both sides of the inequality.

$35 - 15 x + 24 x > 30$

Step 3.2

Add $- 15 x$ and $24 x$ .

$35 + 9 x > 30$

Step 4

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

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Step 4.1

Subtract $35$ from both sides of the inequality.

$9 x > 30 - 35$

Step 4.2

Subtract $35$ from $30$ .

$9 x > - 5$

Step 5

Divide each term in $9 x > - 5$ by $9$ and simplify.

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Step 5.1

Divide each term in $9 x > - 5$ by $9$ .

$\frac{9 x}{9} > \frac{- 5}{9}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $9$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{9 x}{9} > \frac{- 5}{9}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 5}{9}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$x > - \frac{5}{9}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{5}{9}$

Interval Notation:

$(- \frac{5}{9}, \infty)$