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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 76 Page 442

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

x ≥ 29

Practice makes perfect

Before solving the radical inequality, recall that the radicand of a square root must be greater than or equal to 0. sqrt(3x+13) -5≥ 5 Let's start by identifying any values of x for which the inequality is defined.

3x+13 ≥ 0
SubIneq

LHS-13≥RHS-13

3x ≥ - 13
DivIneq

.LHS /3.≥.RHS /3.

x ≥ - 13/3

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

sqrt(3x+13) -5 ≥ 5
AddIneq

LHS+5≥RHS+5

sqrt(3x+13) ≥ 10
RaiseIneq

LHS^2≥RHS^2

( sqrt(3x+13) ) ^2 ≥ 100
PowSqrt

( sqrt(a) )^2 = a

3x+13 ≥ 100
â–¼
Solve for x
SubIneq

LHS-13≥RHS-13

3x ≥ 87
DivIneq

.LHS /3.≥.RHS /3.

x≥ 29

Now we can combine the two intervals.

The intersection of both solutions, which is the final solution set of the given inequality, is x≥ 29.

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Exercises 75 (Page 442)
Exercises 76 (Page 442)
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