Question

name christian kangel date solve each inequality and graph the solution. 1) $\frac{x}{2}+3>9$ 2) $4x + 5leq13$ 3) $7x-19<16$ 4) $\frac{x - 4}{5}geq2$ directions:solve the following word problems using one - s to represent the unknown quantity. 1. seven more than a number is less than 18. find the n 2. five more than a number is greater than 26. find th

Explanation:

Step1: Solve $\frac{x}{2}+3 > 9$

Subtract 3 from both sides.
$\frac{x}{2}+3 - 3>9 - 3$
$\frac{x}{2}>6$
Multiply both sides by 2.
$x > 12$
On the number - line, we have an open circle at 12 and an arrow pointing to the right.

Step2: Solve $4x + 5\leq13$

Subtract 5 from both sides.
$4x+5 - 5\leq13 - 5$
$4x\leq8$
Divide both sides by 4.
$x\leq2$
On the number - line, we have a closed circle at 2 and an arrow pointing to the left.

Step3: Solve $7x - 19 < 16$

Add 19 to both sides.
$7x-19 + 19<16 + 19$
$7x<35$
Divide both sides by 7.
$x < 5$
On the number - line, we have an open circle at 5 and an arrow pointing to the left.

Step4: Solve $\frac{x - 4}{5}\geq2$

Multiply both sides by 5.
$x - 4\geq10$
Add 4 to both sides.
$x\geq14$
On the number - line, we have a closed circle at 14 and an arrow pointing to the right.

Answer:

1. $x>12$; Graph: Open circle at 12, arrow to the right.
2. $x\leq2$; Graph: Closed circle at 2, arrow to the left.
3. $x < 5$; Graph: Open circle at 5, arrow to the left.
4. $x\geq14$; Graph: Closed circle at 14, arrow to the right.