solve and check the following equation:
6(g-6)=5g-2-g
combine like terms, then solve for g
i think the answer comes out to 17
i don't understand how to combine the like terms and how to solve the equation,
6(g-6)=5g-2-g
6(g-6)=5g-2-g
distribute the outside 6 to everything inside the parenthesis
6g-36=5g-2-g
now combine like terms (5g-g)
6g-36=4g-2
combine like terms (get the numbers on one side, and the variables on one side)
6g-4g=-2+36
solve
2g=34
solve for g
g=34/2 = 17
To solve the equation 6(g-6) = 5g-2-g, we need to simplify both sides of the equation and isolate the variable g. Then, we can substitute the obtained value of g back into the original equation to check if it satisfies the equation.
Let's begin by simplifying the equation step by step:
1. Distribute the 6 on the left side:
6g - 36 = 5g - 2 - g
2. Combine like terms on the right side:
6g - 36 = 4g - 2
3. Simplify further by combining the left side terms:
6g - 36 = 4g - 2
4. To isolate the variable g, we can subtract 4g from both sides:
6g - 4g - 36 = 4g - 4g - 2
Simplifying further:
2g - 36 = -2
5. Next, add 36 to both sides of the equation:
2g - 36 + 36 = -2 + 36
Simplifying further:
2g = 34
6. Now, divide both sides by 2 to solve for g:
2g/2 = 34/2
Simplifying further:
g = 17
So the solution to the equation is g = 17.
To check if this solution is valid, substitute g = 17 back into the original equation:
6(g-6) = 5g-2-g
Replace g with 17:
6(17-6) = 5(17)-2-17
Simplifying both sides:
6(11) = 85 - 2 - 17
66 = 66
Since both sides of the equation are equal, the value g = 17 satisfies the original equation. Hence, the solution is correct.