Pre-Algebra Examples

$- 2 (a + 7) < - 3 a + (2 a - 8)$ , $5 a - 2 > 19 - 2 a$

Step 1

Solve $- 2 (a + 7) < - 3 a + 2 a - 8$ for $a$ .

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Step 1.1

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

$- 3 a + 2 a - 8 > - 2 (a + 7)$

Step 1.2

Add $- 3 a$ and $2 a$ .

$- a - 8 > - 2 (a + 7)$

Step 1.3

Simplify $- 2 (a + 7)$ .

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Step 1.3.1

Apply the distributive property.

$- a - 8 > - 2 a - 2 \cdot 7$

Step 1.3.2

Multiply $- 2$ by $7$ .

$- a - 8 > - 2 a - 14$

Step 1.4

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

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Step 1.4.1

Add $2 a$ to both sides of the inequality.

$- a - 8 + 2 a > - 14$

Step 1.4.2

Add $- a$ and $2 a$ .

$a - 8 > - 14$

Step 1.5

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

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Step 1.5.1

Add $8$ to both sides of the inequality.

$a > - 14 + 8$

Step 1.5.2

Add $- 14$ and $8$ .

$a > - 6$

Step 2

Solve $5 a - 2 > 19 - 2 a$ for $a$ .

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Step 2.1

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

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Step 2.1.1

Add $2 a$ to both sides of the inequality.

$5 a - 2 + 2 a > 19$

Step 2.1.2

Add $5 a$ and $2 a$ .

$7 a - 2 > 19$

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 $2$ to both sides of the inequality.

$7 a > 19 + 2$

Step 2.2.2

Add $19$ and $2$ .

$7 a > 21$

Step 2.3

Divide each term in $7 a > 21$ by $7$ and simplify.

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Step 2.3.1

Divide each term in $7 a > 21$ by $7$ .

$\frac{7 a}{7} > \frac{21}{7}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $7$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{7 a}{7} > \frac{21}{7}$

Step 2.3.2.1.2

Divide $a$ by $1$ .

$a > \frac{21}{7}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $21$ by $7$ .

$a > 3$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$a > 3$

Interval Notation:

$(3, \infty)$

Step 4