Solve the System of Inequalities x+8>=9 and x/7<=1

$x + 8 \geq 9$ and $\frac{x}{7} \leq 1$

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

Subtract $8$ from both sides of the inequality.

$x \geq 9 - 8$

Subtract $8$ from $9$ .

$x \geq 1$

Simplify the second inequality.

Multiply both sides by $7$ .

$\frac{x}{7} \cdot 7 \leq 1 \cdot 7$

Simplify.

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{x}{7} \cdot 7 \leq 1 \cdot 7$

Rewrite the expression.

$x \leq 1 \cdot 7$

Simplify the right side.

Multiply $7$ by $1$ .

$x \leq 7$

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

$1 \leq x \leq 7$

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x \leq 7$

Interval Notation:

$[1, 7]$