Finite Math Examples

$7 - 2 (j - 4) > j - 13$

Step 1

Simplify $7 - 2 (j - 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$7 - 2 j - 2 \cdot - 4 > j - 13$

Step 1.1.2

Multiply $- 2$ by $- 4$ .

$7 - 2 j + 8 > j - 13$

Step 1.2

Add $7$ and $8$ .

$- 2 j + 15 > j - 13$

Step 2

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

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Step 2.1

Subtract $j$ from both sides of the inequality.

$- 2 j + 15 - j > - 13$

Step 2.2

Subtract $j$ from $- 2 j$ .

$- 3 j + 15 > - 13$

Step 3

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

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Step 3.1

Subtract $15$ from both sides of the inequality.

$- 3 j > - 13 - 15$

Step 3.2

Subtract $15$ from $- 13$ .

$- 3 j > - 28$

Step 4

Divide each term in $- 3 j > - 28$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 j > - 28$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 j}{- 3} < \frac{- 28}{- 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 j}{- 3} < \frac{- 28}{- 3}$

Step 4.2.1.2

Divide $j$ by $1$ .

$j < \frac{- 28}{- 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

$j < \frac{28}{3}$

Step 5

Convert the inequality to interval notation.

$(- \infty, \frac{28}{3})$

Step 6