Algebra Examples

$a \leq 2 x - 8 \leq b$

Step 1

Solve $2 x - 8 \leq b$ for $x$ .

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Step 1.1

Add $8$ to both sides of the inequality.

$2 x \leq b + 8$

Step 1.2

Divide each term in $2 x \leq b + 8$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x \leq b + 8$ by $2$ .

$\frac{2 x}{2} \leq \frac{b}{2} + \frac{8}{2}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{b}{2} + \frac{8}{2}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{b}{2} + \frac{8}{2}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $8$ by $2$ .

$x \leq \frac{b}{2} + 4$

Step 2

Find the intersection of $a \leq 2 x - 8$ and $x \leq \frac{b}{2} + 4$ .

$x \leq N o (Min i m u m)$

Step 3