Consider the equation 2z−2−−−−−√=5. Which of the following values for z makes the equation true: 11.5, 12.5, or 13.5?
The value of z that makes the equation true is
11.5.
To find the value of z that makes the equation true, we can solve the equation step-by-step.
Given equation: 2z−2−−−−−√=5
Step 1: Add 2 to both sides of the equation.
2z−2−√+2=5+2
Simplifying both sides:
2z−√=7
Step 2: Add √ to both sides of the equation.
2z−√+√=7+√
Simplifying both sides:
2z=7+√
Step 3: Divide both sides of the equation by 2.
(2z)/2=(7+√)/2
Simplifying both sides:
z=(7+√)/2
Now we can substitute the values of 11.5, 12.5, and 13.5 into the equation to see which value makes the equation true.
For z = 11.5:
z = (7 + √)/2
z = (7 + √)/(2)
z ≈ (7 + 3.162)/2
z ≈ 10.162/2
z ≈ 5.081
For z = 12.5:
z = (7 + √)/2
z = (7 + √)/(2)
z ≈ (7 + 3.162)/2
z ≈ 10.162/2
z ≈ 5.081
For z = 13.5:
z = (7 + √)/2
z = (7 + √)/(2)
z ≈ (7 + 3.162)/2
z ≈ 10.162/2
z ≈ 5.081
None of the values 11.5, 12.5, or 13.5 make the equation true.