Solve for x. 5/8(x+1/2)=100 (1 point) Responses 160 1/2 160 and 1 half 62 62 159 1/2 159 and 1 half 63
To solve for x, we will first simplify the equation:
5/8(x+1/2) = 100
To get rid of the fraction, we can multiply both sides of the equation by 8:
8 * 5/8(x+1/2) = 8 * 100
On the left side, the 8 in the numerator cancels out with the 8 in the denominator:
5(x+1/2) = 8 * 100
Next, distribute the 5 to both terms inside the parentheses:
5x + 5/2 = 800
Subtract 5/2 from both sides:
5x = 800 - 5/2
To simplify 800 - 5/2, we can find a common denominator:
800 = 800/1 and 5/2 = 5 * 1/2 = 5/2
So, the equation becomes:
5x = 800 - 5/2
To subtract fractions, we need a common denominator, which in this case is 2:
800 = 800/1 and 5/2 = 10/2
So, the equation becomes:
5x = 800 - 10/2
Which simplifies to:
5x = 800 - 5
Now, subtract 5 from 800:
5x = 795
Finally, divide both sides of the equation by 5 to solve for x:
5x/5 = 795/5
x = 159
Therefore, the solution to the equation is x = 159.
Solve for w.
0.7(w+1.2)=2.1
(1 point)
Responses
-0.9
-0.9
1.8
1.8
4.2
4.2
0.9
To solve for w, we need to isolate w on one side of the equation.
0.7(w+1.2) = 2.1
Let's begin by distributing 0.7 to both terms inside the parentheses:
0.7w + 0.7 * 1.2 = 2.1
Simplifying the expression:
0.7w + 0.84 = 2.1
Next, subtract 0.84 from both sides of the equation:
0.7w = 2.1 - 0.84
0.7w = 1.26
To solve for w, we need to divide both sides of the equation by 0.7:
(0.7w)/0.7 = 1.26/0.7
w = 1.8
Therefore, the solution to the equation is w = 1.8.
To solve for x in the equation 5/8(x + 1/2) = 100, you need to isolate x by following these steps:
Step 1: Distribute the 5/8 to the terms inside the parentheses:
(5/8) * (x + 1/2) = 100
(5/8)x + (5/8)(1/2) = 100
Step 2: Simplify the expression inside the parentheses:
(5/8)x + 5/16 = 100
Step 3: Move the constant term (5/16) to the other side of the equation by subtracting it from both sides:
(5/8)x = 100 - 5/16
Step 4: Simplify the right side of the equation:
(5/8)x = (1600/16) - (5/16)
(5/8)x = 1595/16
Step 5: To get rid of the fraction coefficient (5/8) in front of x, multiply both sides of the equation by the reciprocal of (5/8), which is (8/5):
[(8/5) * (5/8)] * x = [(8/5) * (1595/16)]
Step 6: Simplify both sides:
1 * x = (12760/80)
x = 159.5
Therefore, the value of x in the equation is 159.5.
Note: Some of the options you provided are incorrect. The correct answer is 159.5, not 160.5 or any other fraction value.