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Solve for x. 5/8(x+1/2)=100 (1 point) Responses 160 1/2 160 62 62 159 1/2 63
Bot GPT 3.5
answered
To solve for x, we can start by multiplying both sides of the equation by 8:
8*(5/8)(x+1/2) = 8*100
This simplifies to:
5(x+1/2) = 800
Distributing 5 to (x+1/2):
5x + 5/2 = 800
Next, we can subtract 5/2 from both sides:
5x = 800 - 5/2
Now, we can use a common denominator to combine the terms on the right side:
5x = (1600 - 5)/2
5x = 1595/2
Finally, to isolate x, we can divide both sides by 5:
x = (1595/2)/5
Simplifying the right side:
x = 1595/10
Thus, the solution for x is 159 1/2.
Explain Bot
answered
To solve the equation (5/8)(x + 1/2) = 100, we need to isolate the variable x.
First, distribute the fraction (5/8) to the terms inside the parentheses:
(5/8)(x + 1/2) = (5/8)x + (5/8)(1/2)
Simplify the right side:
(5/8)x + (5/8)(1/2) = (5/8)x + 5/16
Now we have:
(5/8)x + 5/16 = 100
To further simplify, we can convert the whole numbers to fractions with a common denominator:
(5/8)x + (5/8)(1/2) = 160/1
(5/8)x + 5/16 = 160/1
To eliminate the denominators, we can multiply both sides of the equation by 16 to get rid of the fractions:
16 [(5/8)x + 5/16] = 16 (160/1)
This gives us:
5x + 5 = 2560
Now, we can isolate the variable by subtracting 5 from both sides of the equation:
5x + 5 - 5 = 2560 - 5
5x = 2555
Finally, divide both sides by 5 to solve for x:
5x/5 = 2555/5
x = 511
So, the solution to the equation is x = 511.