solve equation g+4/g-2=g-5/g-8
last one still don't get answer my teacher got was 14, however i got 22..
what was my mistake?
Teacher is correct.
(g+4)/(g-2) = (g-5)/(g-8)
(g+4)*(g-8)=(g-5)(g-2)
g^2 -4g -32=g^2-7g+10
3g=42
g=14
To find the mistake, let's go through the steps in solving the equation:
Step 1: Start by expanding the equation:
g + 4 / (g - 2) = g - 5 / (g - 8)
Step 2: Multiply both sides of the equation by (g - 2) and (g - 8) to eliminate the fractions:
(g + 4)(g - 8) = (g - 5)(g - 2)
Step 3: Simplify both sides of the equation:
g^2 - 4g - 32 = g^2 - 7g + 10
Step 4: Combine like terms on both sides of the equation:
-4g - 32 = - 7g + 10
Step 5: Move all the g terms to one side of the equation:
-4g + 7g = 10 + 32
This step contains the mistake. When you move the terms across the equals sign, the signs of the terms also change. So, it should be:
+4g - 7g = 10 + 32
Continuing from the corrected step:
-3g = 42
Step 6: Divide both sides of the equation by -3:
g = 42 / -3
Simplifying the fraction, we get:
g = -14
Therefore, the correct solution is g = -14.
Your mistake was in the sign change when moving the g terms across the equals sign.
To solve the equation g+4/g-2 = g-5/g-8, you need to find the value of g that satisfies the equation. Let's go through the steps to solve it correctly:
1. Start by cross-multiplying to eliminate the denominators:
(g+4)(g-8) = (g-2)(g-5)
Using FOIL (First, Outer, Inner, Last), expand both sides of the equation:
g^2 - 8g + 4g - 32 = g^2 - 5g - 2g + 10
Simplifying further, we have:
g^2 - 4g - 32 = g^2 - 7g + 10
2. Next, cancel out the common terms on both sides of the equation (g^2):
-4g - 32 = -7g + 10
3. Combine like terms on both sides:
-4g + 7g = 10 + 32
3g = 42
4. Divide both sides of the equation by 3 to isolate g:
g = 42/3
g = 14
So the correct solution is g = 14. Therefore, your teacher's answer of 14 is correct.
If you obtained 22 as your answer, it means there might have been a mistake made during simplification or calculations. Review your steps and make sure you correctly expanded the equation, combined like terms, and solved for g.