Algebra 2

Chapter 1.5 Solving Inequalities

Target Goals:1. Solve one-step and multi-step inequalities2. Graph the solution set on an number line3. Express the solution set in interval notation

What do the symbols mean?

< > ≤ ≥

less than greater than

more than

less than or equal to

no more than

greater than or equal to

more than or equal to

at least

Equations vs. Inequalities

Similarities• Isolate the variable when

solving• Use the same properties of

equalities when solving

Differences• Different signs (= vs. >, <, ≥,

or ≤)• When multiplying or

dividing both sides by a negative number, remember to switch the direction of the inequality sign.

Solve each inequality and graph the solution set on a number line. Express the solution set in interval notation.

Ex 1) 4y – 3 < 5y + 2 4y – 3 < 5y + 2

Solve each inequality and graph the solution set on a number line. Express the solution set in interval

notation.

Ex 2) 12 ≥ -0.3x

Solve each inequality and graph the solution set on a number line. Express the solution set in interval

notation.

Ex 3) 7

2

xx

ApplicationsEx 4) Javier has at most $15.00 to spend

today. He buys a bag of pretzels and a bottle of juice for $1.59. If gasoline at this store costs $2.89 per gallon, how many gallons of gasoline, to the nearest tenth of a gallon, can Javier buy for his car?

ApplicationsEx 5) Jin is selling advertising space in Central City

Magazine to local businesses. Jin earns 3% commission for every advertisement he sells plus a salary of $250 per week. If the average amount of money that a business spends on an advertisement is $500, how many advertisements must he sell each week to make a salary of at least $700 that week?

Target Goals

1. Solve one-step and multi-step inequalities– (ex 1, 2, 3, 4, & 5)

2. Graph the solution set on an number line– (ex 1, 2, & 3)

3. Express the solution set in interval notation– (ex 1, 2, & 3)