Solve the System of Inequalities 6b-1<=41 or 2b+1>=11

$6 b - 1 \leq 41$ or $2 b + 1 \geq 11$

Step 1

Simplify the first inequality.

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

Add $1$ to both sides of the inequality.

$6 b \leq 41 + 1$

Add $41$ and $1$ .

$6 b \leq 42$

Divide each term in $6 b \leq 42$ by $6$ and simplify.

Divide each term in $6 b \leq 42$ by $6$ .

$\frac{6 b}{6} \leq \frac{42}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 b}{6} \leq \frac{42}{6}$

Divide $b$ by $1$ .

$b \leq \frac{42}{6}$

Simplify the right side.

Divide $42$ by $6$ .

$b \leq 7$

Step 2

Simplify the second inequality.

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

Subtract $1$ from both sides of the inequality.

$2 b \geq 11 - 1$

Subtract $1$ from $11$ .

$2 b \geq 10$

Divide each term in $2 b \geq 10$ by $2$ and simplify.

Divide each term in $2 b \geq 10$ by $2$ .

$\frac{2 b}{2} \geq \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 b}{2} \geq \frac{10}{2}$

Divide $b$ by $1$ .

$b \geq \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$b \geq 5$

Step 3

The union consists of all of the elements that are contained in each interval.

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Step 5

Solve the System of Inequalities 6b-1<=41 or 2b+1>=11

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