Solve: (x+5 1/2)0.75=5/8
Please show all steps
This anwser does not make sense. I am very confused on how to do this problem. I have checked multiple sites and the anwser is always something point something something something. I need help with this problem.
To solve the equation (x + 5 1/2) * 0.75 = 5/8, you can follow the steps below:
Step 1: Distribute the 0.75 to (x + 5 1/2):
0.75 * x + 0.75 * 5 1/2 = 5/8
Step 2: Simplify the expression on the left side:
0.75x + 0.75 * 11/2 = 5/8
To multiply 0.75 and 11/2, you can multiply the numerators together (0.75 * 11) and multiply the denominators together (1 * 2).
Step 3: Continue simplifying the expression:
0.75x + 8.25/2 = 5/8
To simplify 8.25/2, you divide the numerator, 8.25, by the denominator, 2. This gives you 4.125.
Step 4: Substitute the simplified expression back into the equation:
0.75x + 4.125 = 5/8
Step 5: To get rid of the fraction on the right side, multiply both sides of the equation by the reciprocal of 8/1, which is 1/8:
(1/8) * (0.75x + 4.125) = (1/8) * (5/8)
Step 6: Simplify the equation:
0.75x/8 + 4.125/8 = 5/64
To divide 0.75x by 8, you divide the numerator, 0.75x, by the denominator, 8. This gives you 0.09375x.
To divide 4.125 by 8, you divide the numerator, 4.125, by the denominator, 8. This gives you 0.515625.
Step 7: Substitute the simplified expressions back into the equation:
0.09375x + 0.515625 = 5/64
Step 8: To isolate x, subtract 0.515625 from both sides of the equation:
0.09375x = 5/64 - 0.515625
To subtract fractions, you need to have a common denominator. The denominator 64 can serve as the common denominator for both 5/64 and 0.515625 by multiplying the numerator and denominator of 5/64 by 1 (in the form of 64/64).
5/64 - 0.515625 = 5/64 - (0.515625 * 64/64)
= 5/64 - 32.984375/64
= (5 - 32.984375)/64
= -27.984375/64
Step 9: Simplify the equation:
0.09375x = -27.984375/64
Step 10: To isolate x, divide both sides of the equation by 0.09375:
(0.09375x)/(0.09375) = (-27.984375/64)/(0.09375)
Step 11: Simplify the equation:
x = -27.984375/64 / 0.09375
To divide fractions, we multiply the numerator by the reciprocal of the denominator:
x = (-27.984375/64) * (1/0.09375)
Simplify:
x = -27.984375/64 * 1/0.09375
x = -28/64 * 1/0.09375
x = -7/16 * 1/0.09375
x = -7/16 * 16/18
x = -7/18
So the solution to the equation (x + 5 1/2) * 0.75 = 5/8 is x = -7/18.
(x+5 1/2)0.75=5/8
(x + 5.5)0.75 = 0.625
0.75x + 4.125 = 0.625
0.75x = -3.5
x = -4.666667 = -4 2/3