Final answer:
To solve these linear equations, simplify both sides of the equation, combine like terms, isolate the variable, and solve for x.
Step-by-step explanation:
a) -2x - 4 = -9 + 3x:
First, we can simplify both sides of the equation by combining like terms. We get -2x - 4 = -9 + 3x.
Next, we can move all the x-terms to one side of the equation and the constant terms to the other side. This gives us -2x - 3x = -9 + 4.
Now, we can combine like terms again to solve for x. We get -5x = -5.
Finally, we can solve for x by dividing both sides of the equation by -5. This gives us x = 1.
b) 5(1 + 4x) = 65:
First, we can distribute the 5 to both terms inside the parentheses. This gives us 5 + 20x = 65.
Next, we can subtract 5 from both sides of the equation to isolate the variable. This gives us 20x = 60.
Finally, we can solve for x by dividing both sides of the equation by 20. This gives us x = 3.
c) 2x + 5 = 8x - 7:
First, we can simplify both sides of the equation by combining like terms. We get 2x + 5 = 8x - 7.
Next, we can move all the x-terms to one side of the equation and the constant terms to the other side. This gives us 2x - 8x = -7 - 5.
Now, we can combine like terms again to solve for x. We get -6x = -12.
Finally, we can solve for x by dividing both sides of the equation by -6. This gives us x = 2.