Question

A) 3x-7=2(x-4)B) 3x-7=3(x-2)-1

Answer 1

A) 3x-7=2(x-4)
3x-7 = 2x-8
3x-2x = -8+7
x = -1
B) 3x-7=3(x-2)-1
3x-7 = 3x-6-1
3x-7 = 3x-7
3x-3x = -7+7
0x = 0
x - любое число

Answer 2

A) 3x - 7 = 2(x - 4)

To solve this equation, we'll follow a series of steps to isolate the variable x on one side of the equation.

Step 1: Distribute the 2 on the right side of the equation: 3x - 7 = 2x - 8 Step 2: Move all terms containing x to the left side of the equation by subtracting 2x from both sides: 3x - 2x - 7 = -8 Simplifying the left side of the equation gives us: x - 7 = -8 Step 3: Move the constant term to the right side of the equation by adding 7 to both sides: x - 7 + 7 = -8 + 7 Simplifying the right side of the equation gives us: x = -1

So, the solution to the equation 3x - 7 = 2(x - 4) is x = -1.

B) 3x - 7 = 3(x - 2) - 1

To solve this equation, we'll again follow a series of steps to isolate the variable x on one side of the equation.

Step 1: Distribute the 3 on the right side of the equation: 3x - 7 = 3x - 6 - 1 Step 2: Simplify the equation by combining like terms on both sides: 3x - 7 = 3x - 7

At this point, we can see that both sides of the equation are identical. This means that the equation is an identity and any value of x will satisfy the equation. In other words, this equation has infinitely many solutions.

Therefore, the solution to the equation 3x - 7 = 3(x - 2) - 1 is x can be any real number.