I need help solving equations with the variable on both sides:
3(d-8)-5=9(d+2)+1
please help
3(d-8)-5=9(d+2)+1
Do the multiplication, then combine like terms:
3d - 24 - 5 = 9d + 18 + 1
-29 -18 -1 = 9d - 3d
-48 = 6d
-8 = d
50q-43=52q-81
To solve an equation with the variable on both sides, you need to simplify each side of the equation, move the variable terms to one side, and the constant terms to the other side.
Let's solve the equation step by step:
1. Start by distributing the multiplication to simplify each side of the equation:
3(d-8) - 5 = 9(d+2) + 1
3d - 24 - 5 = 9d + 18 + 1
2. Combine like terms on each side:
3d - 29 = 9d + 19
3. Now, let's move the variable terms to one side (left side) and the constant terms to the other side (right side). To do this, we'll subtract 3d from both sides and add 29 to both sides:
3d - 9d - 29 + 29 = 9d - 3d + 19 + 29
-6d = 6d + 48
4. Combine like terms on each side:
-6d = 15d + 48
5. Next, move all the variable terms to one side and the constant terms to the other side by subtracting 15d from both sides:
-6d - 15d = 15d + 48 - 15d
-21d = 48
6. Divide both sides by -21 to isolate the variable:
(-21d) / (-21) = 48 / (-21)
d = -2.2857 (rounded to 4 decimal places)
So, the solution to the equation is d ≈ -2.2857.
By following these step-by-step instructions, you can solve equations with the variable on both sides.