Solve for x.
5/8(x+1/2)=100
(1 point)
Responses
1601/2
160 and 1 half
62
62
159 1/2
159 and 1 half
63
To solve for x, first distribute the 5/8 to the terms inside the parentheses:
5/8(x+1/2) = 100
(5/8 * x) + (5/8 * 1/2) = 100
(5/8)(x) + 5/16 = 100
Next, subtract 5/16 from both sides of the equation:
(5/8)(x) = 100 - 5/16
(5/8)(x) = 160
To isolate x, divide both sides of the equation by 5/8:
x = (160)/(5/8)
x = 160 * (8/5)
x = 256
Therefore, the solution is x = 256.
5/8(x+1/2)=100
(1 point)
Responses
1601/2
160 and 1 half
62
62
159 1/2
159 and 1 half
63
To solve for x, first distribute the 5/8 to the terms inside the parentheses:
5/8(x+1/2) = 100
Multiply 5/8 by x and 5/8 by 1/2:
(5/8)x + (5/8)(1/2) = 100
Simplify:
(5/8)x + 5/16 = 100
To isolate x, subtract 5/16 from both sides:
(5/8)x = 100 - 5/16
Find a common denominator for 5/16 and 100:
(5/8)x = 1600/16 - 5/16
Combine the fractions on the right side:
(5/8)x = 1595/16
To solve for x, multiply both sides by the reciprocal of 5/8, which is 8/5:
x = (1595/16) * (8/5)
Multiply the numerators and denominators:
x = (1595 * 8) / (16 * 5)
Simplify:
x = 12760 / 80
To reduce the fraction, divide the numerator and denominator by the greatest common divisor, which is 80:
x = 159.5
Therefore, the solution is x = 159.5.
To solve for x in the equation 5/8(x+1/2) = 100, you can start by multiplying both sides of the equation by 8/5 to eliminate the fraction:
(8/5) * 5/8(x+1/2) = (8/5) * 100
On the left side, the 5/8 and 8/5 cancel out, leaving us with just (x+1/2):
x + 1/2 = (8/5) * 100
Next, simplify the right side of the equation:
x + 1/2 = 800/5
800 divided by 5 equals 160, so the equation becomes:
x + 1/2 = 160
To isolate x, subtract 1/2 from both sides of the equation:
x = 160 - 1/2
To subtract fractions, you need a common denominator. The common denominator of 2 and 1 is 2. Rewrite 160 as a fraction with a denominator of 2:
x = 320/2 - 1/2
Combine the fractions:
x = (320 - 1)/2
x = 319/2
So the solution for x is 319/2, which can also be written as 159 and 1/2.