Solve Linear Inequalities: example 2.74

Solve the inequality $8 p + 3 (p - 12) > 7 p - 28$ , graph the solution on the number line, and write the solution in interval notation.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the inequality $9 y + 2 (y + 6) > 5 y - 24$ , graph the solution on the number line, and write the solution in interval notation.

How did it go?

Simplify each side as much as possible.	$8 p + 3 (p - 12) > 7 p - 28$
Distribute.	$8 p + 3 p - 36 > 7 p - 28$
Combine like terms.	$11 p - 36 > 7 p - 28$
Subtract $7 p$ from both sides to collect the variables on the left.	$11 p - 36 - 7 p > 7 p - 28 - 7 p$
Simplify.	$4 p - 36 > −28$
Add 36 to both sides to collect the constants on the right.	$4 p - 36 + 36 > −28 + 36$
Simplify.	$4 p > 8$
Divide both sides of the inequality by 4; the inequality stays the same.	$\frac{4 p}{4} > \frac{8}{4}$
Simplify.	$p > 2$
Graph the solution on the number line.
Write the solution in interal notation.	$(2, ∞)$

Simplify each side as much as possible.	$8 p + 3 (p - 12) > 7 p - 28$
Distribute.	$8 p + 3 p - 36 > 7 p - 28$
Combine like terms.	$11 p - 36 > 7 p - 28$
Subtract $7 p$ from both sides to collect the variables on the left.	$11 p - 36 - 7 p > 7 p - 28 - 7 p$
Simplify.	$4 p - 36 > −28$
Add 36 to both sides to collect the constants on the right.	$4 p - 36 + 36 > −28 + 36$
Simplify.	$4 p > 8$
Divide both sides of the inequality by 4; the inequality stays the same.	$\frac{4 p}{4} > \frac{8}{4}$
Simplify.	$p > 2$
Graph the solution on the number line.
Write the solution in interal notation.	$(2, ∞)$