Example 2.76 from Elementary Algebra, 2.7 Solve Linear Inequalities

Solve Linear Inequalities: example 2.76

Solve the inequality $\frac{1}{3} a - \frac{1}{8} a > \frac{5}{24} a + \frac{3}{4}$ , 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 $\frac{1}{4} x - \frac{1}{12} x > \frac{1}{6} x + \frac{7}{8}$ , graph the solution on the number line, and write the solution in interval notation.

How did it go?


Multiply both sides by the LCD, 24, to clear the fractions.
Simplify.
Combine like terms.
Subtract $5 a$ from both sides to collect the variables on the left.
Simplify.
The statement is false!	The inequality is a contradiction.
	There is no solution.
Graph the solution on the number line.
Write the solution in interval notation.	There is no solution.


Multiply both sides by the LCD, 24, to clear the fractions.
Simplify.
Combine like terms.
Subtract $5 a$ from both sides to collect the variables on the left.
Simplify.
The statement is false!	The inequality is a contradiction.
	There is no solution.
Graph the solution on the number line.
Write the solution in interval notation.	There is no solution.

Solve Linear Inequalities: example 2.76

Solution

Your turn

Solve Linear Inequalities: example 2.76

Solution

Your turn