I have to solve sqrt(2x-7) >=5
answers would be x>=16
x>=7/2
7/2<=x<=16
x<=16
I don't get this concept at all and I have 20 of these kinds of problems for homeowrk-can someone direct me how to start or give me an example or just help please? I really need to figure out this concept
Thank you
√(2x-7) > 5
Since both left and right side are positive we don't have to worry about any changes in direction of the inequality sign.
So square both sides
2x-7 ≥ 25
2x ≥ 32
x ≥ 16
and of course for √(2x-7) to be a real number, the inside must be ≥ 0
that is, 2x-7 ≥ 0
2x ≥ 7
x ≥ 7/2
so now you have x ≥ 7/2 AND x ≥ 16
which set of numbers satisfies BOTH conditions?
It would be x ≥ 16
(take x = 5 for an example
it satisfies the first condition, in that it is ≥ 7/2
but does not work for the original inequation. )
Thank you for the detailed example-I can really use those to figure out the rest of my homeowrk-I should be good now
Thanks again
welcome, come back if you run into more problems.
sqrt(2x-7) >= 5
What don't you understand?
to solve, square both sides to get rid of the radical
2x - 7 >= 25
2x >= 32
x >= 16
Sure, I can help you understand how to solve this type of inequality. Let's start by breaking down the steps to solve the inequality sqrt(2x-7) >= 5.
Step 1: Isolate the square root expression. To do this, we need to get rid of the square root by squaring both sides of the inequality. Squaring both sides will remove the square root symbol.
(sqrt(2x-7))^2 >= 5^2
2x - 7 >= 25
Step 2: Solve the resulting equation. Now that the square root is eliminated, we have a linear inequality to solve.
2x - 7 >= 25
Step 3: Isolate the variable. To isolate the variable x, we need to add 7 to both sides of the inequality.
2x >= 25 + 7
2x >= 32
Step 4: Divide by the coefficient of x. Divide both sides of the inequality by 2.
x >= 32/2
x >= 16
Therefore, the solution to the inequality sqrt(2x-7) >= 5 is x >= 16.
Now, let's also find the solution in interval notation, which may be required for some problems.
We know that x >= 16, so the lower bound is 16. To find the upper bound, we need to consider the original inequality and solve for x once again.
sqrt(2x-7) >= 5
We solve for x by isolating the square root expression:
sqrt(2x-7) = 5
Square both sides:
2x - 7 = 25
2x = 25 + 7
2x = 32
x = 32/2
x = 16
So, x = 16 is also a possible solution.
Therefore, the solution in interval notation is 16 <= x <= 16 or simply x = 16.
I hope this explanation helps you tackle similar problems. Let me know if you have any further questions!