Question:-
Find the value of x in the following equation:
3(2x - 5) + 2(3x + 7) = 4(x + 3) + 10
Solution:-
Given equation:
3(2x - 5) + 2(3x + 7) = 4(x + 3) + 10
Step 1:
Distribute the terms on both sides of the equation:
On the left side, distribute the coefficients 3 and 2:
6x - 15 + 6x + 14 = 4(x) + 4(3) + 10
Simplify the expressions:
12x - 1 = 4x + 12 + 10
Step 2:
Move all the terms with x to one side of the equation and the constants to the other side: Subtract 4x from both sides:
12x - 4x - 1 = 4x - 4x + 12 + 10
Simplify the expressions:
8x - 1 = 22
Step 3:
Move the constant term to the other side by adding 1 to both sides:
8x - 1 + 1 = 22 + 1
Simplify the expressions:
8x = 23
Step 4:
Solve for x by dividing both sides by 8:
x = 23 / 8
Step 5:
Simplify the fraction (if possible):
x ≈ 2.875
So, the value of x in the given equation is approximately 2.875.
