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McGraw Hill Glencoe Algebra 2, 2012
MH
McGraw Hill Glencoe Algebra 2, 2012 View details
Study Guide and Review
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Exercise 75 Page 442

Start by identifying the values of x for which the inequality is defined.

1/3 ≤ x < 10/3

Practice makes perfect

Before solving the radical inequality, recall that the radicand of a square root must be greater than or equal to 0. 2+sqrt(3x-1) < 5 Let's start by identifying any values of x for which the inequality is defined.

3x-1 ≥ 0
AddIneq

LHS+1≥RHS+1

3x ≥ 1
DivIneq

.LHS /3.≥.RHS /3.

x ≥ 1/3

After we solve the given inequality, we can combine the above information to obtain the final solution set. Let's now solve the inequality.

2+sqrt(3x-1) < 5
SubIneq

LHS-2

sqrt(3x-1) < 3
RaiseIneq

LHS^2

( sqrt(3x-1) ) ^2 < 9
PowSqrt

( sqrt(a) )^2 = a

3x-1 < 9
â–¼
Solve for x
AddIneq

LHS+1

3x < 10
DivIneq

.LHS /3.<.RHS /3.

x<10/3

Now we can combine the two intervals.

The intersection of both solutions, which is the final solution set of the given inequality, is 13 ≤ x < 103.

Subchapter links expand_more
arrow_right Exercises p.438-442
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Exercises 22 (Page 439)
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Exercises 75 (Page 442)
Exercises 76 (Page 442)
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