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Solve the equation 3.6g + 4 = 1.6g + 16.
a. Find the value of g.
b. Explain how you can check that the value you found for g is correct. If your check does not work, explain why not.
a. g = __
(Simplify your answer. Type an integer or a decimal.)
To solve the equation (3.6g + 4 = 1.6g + 16), we will isolate (g).
Step 1: Move all terms involving (g) to one side and constant terms to the other side.
Subtract (1.6g) from both sides:
[3.6g – 1.6g + 4 = 16]
This simplifies to:
[2g + 4 = 16]
Step 2: Subtract 4 from both sides to isolate terms with (g):
[2g = 16 – 4]
[2g = 12]
Step 3: Divide both sides by 2 to solve for (g):
[g = frac{12}{2} = 6]
So, the value of (g) is:
a. (g = 6)
Step 4: Check the solution.
To check if (g = 6) is correct, substitute (6) back into the original equation:
Left side:
[3.6(6) + 4 = 21.6 + 4 = 25.6]
Right side:
[1.6(6) + 16 = 9.6 + 16 = 25.6]
Since both sides equal (25.6), the solution
To solve the equation (3.6g + 4 = 1.6g + 16), follow these steps:
Step 1: Isolate the variable (g)
First, get all the terms containing (g) on one side and the constant terms on the other side. Subtract (1.6g) from both sides:
[
3.6g – 1.6g + 4 = 16
]
Simplifying this gives:
[
2g + 4 = 16
]
Step 2: Move the constant
Next, subtract 4 from both sides:
[
2g = 16 – 4
]
This simplifies to:
[
2g = 12
]
Step 3: Solve for (g)
Now, divide both sides by 2:
[
g = frac{12}{2}
]
Thus, we have:
[
g = 6
]
a. The value of (g) is 6.
b. To check if this value is correct, substitute (g) back into the original equation:
[
3.6(6) + 4 = 1.6(6) + 16
]
Calculating both sides:
Left side:
[
3.6 times 6 + 4 = 21.6