Question

solve the equation below. whats the value of g?
\frac{2(15g + 5)}{10} = -5g + 3
\frac{15g + 5}{5} = -5g + 3
3g + 1 = -5g + 3
subtract 5g from both sides
add 5g to each side
divide each side by 5g
multiply each side by 5g

Explanation:

Step1: Analyze the equation

We have the equation \(3g + 1=-5g + 3\). To solve for \(g\), we want to get all the \(g\) terms on one side.

Step2: Determine the operation

To move the \(-5g\) from the right - hand side to the left - hand side, we use the addition property of equality. If we add \(5g\) to both sides, we can eliminate the \(-5g\) on the right.
Adding \(5g\) to both sides: \((3g + 1)+5g=(-5g + 3)+5g\)
Simplifying the left - hand side: \(3g+5g + 1=8g + 1\)
Simplifying the right - hand side: \(-5g+5g + 3=3\)
The equation becomes \(8g + 1 = 3\), which is a simpler equation to solve for \(g\). The other operations: subtracting \(5g\) would give \(3g + 1-5g=-5g + 3-5g\) or \(-2g + 1=-10g + 3\), which is more complicated. Dividing or multiplying by \(5g\) would introduce more complexity as there is a constant term (\(1\) and \(3\)) and it is not a valid way to solve this linear equation for \(g\) at this stage.

Answer:

Add 5g to each side