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3x-5(3x-7)= 2(x+9)+45
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To solve this equation, we'll follow these steps:
Step 1: Distribute the terms on both sides of the equation.
Step 2: Combine like terms.
Step 3: Simplify the equation.
Step 4: Solve for x.
Let's go through this step by step:
Step 1: Distribute the terms on both sides of the equation.
On the left side, we have:
3x - 5(3x - 7)
Apply the distributive property to the expression inside the parentheses:
= 3x - 15x + 35
On the right side, we have:
2(x + 9) + 45
Apply the distributive property to 2(x + 9):
= 2x + 18 + 45
Simplify the right side:
= 2x + 63
Now our equation becomes:
3x - 15x + 35 = 2x + 63
Step 2: Combine like terms.
Combine the x terms on the left side:
-12x + 35 = 2x + 63
Step 3: Simplify the equation.
To simplify the equation further, let's isolate the x terms on one side:
Subtract 2x from both sides:
-12x - 2x + 35 = 2x - 2x + 63
-14x + 35 = 63
Step 4: Solve for x.
Next, isolate the x term by subtracting 35 from both sides:
-14x + 35 - 35 = 63 - 35
-14x = 28
Finally, divide both sides of the equation by -14:
x = 28 / -14
x = -2
Therefore, the solution to the equation is x = -2.