Algebra Examples

$48 \geq 6 - 7 a$

Step 1

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

$6 - 7 a \leq 48$

Step 2

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

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Step 2.1

Subtract $6$ from both sides of the inequality.

$- 7 a \leq 48 - 6$

Step 2.2

Subtract $6$ from $48$ .

$- 7 a \leq 42$

Step 3

Divide each term in $- 7 a \leq 42$ by $- 7$ and simplify.

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Step 3.1

Divide each term in $- 7 a \leq 42$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 a}{- 7} \geq \frac{42}{- 7}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 7$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 7 a}{- 7} \geq \frac{42}{- 7}$

Step 3.2.1.2

Divide $a$ by $1$ .

$a \geq \frac{42}{- 7}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $42$ by $- 7$ .

$a \geq - 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$a \geq - 6$

Interval Notation:

$[- 6, \infty)$