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McGraw Hill Glencoe Algebra 1, 2012 View details

3. Solving Multi-Step Inequalities

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Exercise 33 Page 301

What can you do to isolate a variable in an inequality?

Solution Set: {t|t≥-1}
Graph:

Practice makes perfect

Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must reverse the inequality sign.

7+t≤ 2(t+3)+2

Distr

Distribute 2

7+t≤ 2t+6+2

AddTerms

Add terms

7+t≤2t+8

SubIneq

LHS-t≤RHS-t

7≤ t+8

SubIneq

LHS-8≤RHS-8

-1≤ t

RearrangeIneq

Rearrange inequality

t≥-1

This tells us that all values greater than or equal to -1 satisfy the inequality. Knowing this, let's write the solution set. {t|t≥ - 1} Now, let's demonstrate the inequality by graphing the solution set on a number line. Notice that, since the inequality is non-strict, t can equal -1. We show this with a closed circle on the number line.

Subchapter links

Check Your Understanding p.300

Practice and Problem Solving p.301-302

H.O.T. Problems p.302

Standardized Test Practice p.303

Spiral Review p.303

Skills Review p.303

Exercise 33 Page 301

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