There are two solutions to | 16x - 5 | = 3. The greatest solution is ___.
Since the expression, 16x - 5, can be either positive or negative, solve for both.
16x - 5 = 3
16x = 8
x = .5
-(16x - 5) = 3
-16x + 5 = 3
-16x = -2
x = 1/8
You can decide which is "greatest."
I hope this helps. Thanks for asking.
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To find the greatest solution to the equation |16x - 5| = 3, you need to solve the equation for both cases when the expression 16x - 5 is positive and when it is negative.
Step 1:
When 16x - 5 is positive:
16x - 5 = 3
Step 2:
Solving this equation for x, we can add 5 to both sides:
16x - 5 + 5 = 3 + 5
16x = 8
Step 3:
Divide both sides of the equation by 16 to isolate x:
16x/16 = 8/16
x = 0.5
So, when 16x - 5 is positive, x = 0.5.
Step 4:
When 16x - 5 is negative, we need to change the equation by negating the expression:
-(16x - 5) = 3
Step 5:
Distribute the negative sign inside the parentheses:
-16x + 5 = 3
Step 6:
Subtract 5 from both sides of the equation:
-16x + 5 - 5 = 3 - 5
-16x = -2
Step 7:
Divide both sides of the equation by -16:
(-16x)/-16 = (-2)/-16
x = 1/8
So, when 16x - 5 is negative, x = 1/8.
Step 8:
To find the greatest solution between 0.5 and 1/8, you can compare the values.
0.5 is greater than 1/8, so the greatest solution to the equation |16x - 5| = 3 is x = 0.5.
I hope this step-by-step explanation helps you to understand the solution method. Let me know if you have any further questions!