Solve. 6(x + 9) + 4x = 5x – 6
To solve the equation 6(x + 9) + 4x = 5x - 6, we will follow these steps:
Step 1: Distribute and simplify.
Start by distributing the 6 to both terms inside the parentheses: 6 * x + 6 * 9.
This becomes 6x + 54.
So the equation becomes: 6x + 54 + 4x = 5x - 6.
Step 2: Combine like terms.
On the left side, combine the terms with 'x': 6x + 4x = 10x.
So the equation simplifies to: 10x + 54 = 5x - 6.
Step 3: Move all terms involving 'x' to one side.
To do this, subtract 5x from both sides of the equation:
10x + 54 - 5x = 5x - 6 - 5x.
Simplifying further, we have: 5x + 54 = -6.
Step 4: Isolate 'x'.
To isolate the 'x' term, we need to move the constant term (54 in this case) to the other side.
Subtract 54 from both sides: 5x + 54 - 54 = -6 - 54.
This simplifies to: 5x = -60.
Step 5: Solve for 'x'.
To solve for 'x', divide both sides of the equation by the coefficient of 'x' (which is 5 in this case).
Dividing both sides by 5, we get: (5x)/5 = -60/5.
Simplifying further, we find: x = -12.
Therefore, the solution to the equation 6(x + 9) + 4x = 5x - 6 is x = -12.