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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 80 Page 442

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

x ≥ 3/2

Practice makes perfect

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

2x-3 ≥ 0
AddIneq

LHS+3≥RHS+3

2x ≥ 3
DivIneq

.LHS /2.≥.RHS /2.

x ≥ 3/2

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

3+sqrt(2x-3) ≥ 3
SubIneq

LHS-3≥RHS-3

sqrt(2x-3) ≥ 0
RaiseIneq

LHS^2≥RHS^2

( sqrt(2x-3) ) ^2 ≥ 0
PowSqrt

( sqrt(a) )^2 = a

2x-3 ≥ 0
â–¼
Solve for x
AddIneq

LHS+3≥RHS+3

2x ≥ 3
DivIneq

.LHS /2.≥.RHS /2.

x ≥ 3/2

Now we can combine the two intervals.

The intersection of both solutions, which is the final solution set of the given inequality, is x ≥ 32.

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arrow_right Exercises p.438-442
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