Algebra Examples

$- 4 a + 13 \geq 29$ and $10 < 6 a - 14$

Step 1

Simplify the first inequality.

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Step 1.1

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

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Step 1.1.1

Subtract $13$ from both sides of the inequality.

$- 4 a \geq 29 - 13$ and $10 < 6 a - 14$

Step 1.1.2

Subtract $13$ from $29$ .

$- 4 a \geq 16$ and $10 < 6 a - 14$

Step 1.2

Divide each term in $- 4 a \geq 16$ by $- 4$ and simplify.

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Step 1.2.1

Divide each term in $- 4 a \geq 16$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 a}{- 4} \leq \frac{16}{- 4}$ and $10 < 6 a - 14$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 4 a}{- 4} \leq \frac{16}{- 4}$ and $10 < 6 a - 14$

Step 1.2.2.1.2

Divide $a$ by $1$ .

$a \leq \frac{16}{- 4}$ and $10 < 6 a - 14$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $16$ by $- 4$ .

$a \leq - 4$ and $10 < 6 a - 14$

Step 2

Simplify the second inequality.

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Step 2.1

Rewrite so $a$ is on the left side of the inequality.

$a \leq - 4$ and $6 a - 14 > 10$

Step 2.2

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

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Step 2.2.1

Add $14$ to both sides of the inequality.

$a \leq - 4$ and $6 a > 10 + 14$

Step 2.2.2

Add $10$ and $14$ .

$a \leq - 4$ and $6 a > 24$

Step 2.3

Divide each term in $6 a > 24$ by $6$ and simplify.

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Step 2.3.1

Divide each term in $6 a > 24$ by $6$ .

$a \leq - 4$ and $\frac{6 a}{6} > \frac{24}{6}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $6$ .

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Step 2.3.2.1.1

Cancel the common factor.

$a \leq - 4$ and $\frac{6 a}{6} > \frac{24}{6}$

Step 2.3.2.1.2

Divide $a$ by $1$ .

$a \leq - 4$ and $a > \frac{24}{6}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $24$ by $6$ .

$a \leq - 4$ and $a > 4$

Step 3

The intersection consists of the elements that are contained in both intervals.

No solution