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Pearson Algebra 1 Common Core, 2011 View details

4. Solving Multi-Step Inequalities

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Exercise 13 Page 190

Begin by isolating r.

r≥3.5

Practice makes perfect

Let's isolate r to solve the inequality.

9≤-12+6r

AddIneq

LHS+12≤RHS+12

21≤6r

DivIneq

.LHS /6.≤.RHS /6.

21/6≤ r

WriteDec

Write as a decimal

3.5≤ r

RearrangeIneq

Rearrange inequality

r≥3.5

The solution r≥3.5 means that any number greater than or equal to 3.5 will satisfy the inequality.

Checking Our Answer

Let's check this by choosing an arbitrary value for r and plugging it into the original inequality. Let's choose 10 for r. Since 10 is greater than 3.5, we expect the result to be true.

9≤-12+6r

Substitute

r= 10

9\stackrel{?}\leq\text{-}12+6\cdot {\color{#0000FF}{10}}

Multiply

9\stackrel{?}\leq\text{-}12+60

AddTerms

Add terms

9≤48

This result is true, so our inequality is correct for this test value.