I need help with the below math problem. I have to write out the steps to show the answer.
2(x - 14) + 3 = 7x + 5
2(x - 14) + 3 = 7x + 5
2x - 28 + 3 = 7x + 5
-5x = 30
x = -6
I understand the second step but how did you get the third answer?
I subtracted 7x from both sides of the equation.
I added 25 to both sides.
To solve the equation 2(x - 14) + 3 = 7x + 5 and show the steps, we will follow a systematic approach known as the order of operations. Here are the steps to solve the equation:
Step 1: Distribute the 2 to the terms inside the parentheses. This can be done by multiplying the 2 by both x and -14. We get:
2x - 28 + 3 = 7x + 5
Step 2: Combine like terms on both sides of the equation. On the left side, combine 2x and -28 to get 2x - 28 + 3 = 2x - 25. On the right side, we have 7x + 5, so the equation becomes:
2x - 25 = 7x + 5
Step 3: Isolate the variable terms on one side of the equation. To do this, subtract 2x from both sides:
2x - 2x - 25 = 7x - 2x + 5
Simplifying this equation, we get:
-25 = 5x + 5
Step 4: Continue to isolate the variable by subtracting 5 from both sides:
-25 - 5 = 5x + 5 - 5
This simplifies to:
-30 = 5x
Step 5: Solve for x by dividing both sides of the equation by 5:
-30 / 5 = 5x / 5
This simplifies to:
-6 = x
So the value of x that solves the equation 2(x - 14) + 3 = 7x + 5 is x = -6.