solve the equation and then check for extraneous solutions 4(3×+4)=4×+8
To solve the equation, we'll begin by distributing 4 to the terms within the parentheses:
4(3x + 4) = 4x + 8
12x + 16 = 4x + 8
Next, we'll isolate the x terms on one side by subtracting 4x from both sides:
12x - 4x + 16 = 4x - 4x + 8
8x + 16 = 8
Simplifying further, we'll subtract 16 from both sides:
8x + 16 - 16 = 8 - 16
8x = -8
To solve for x, we'll divide both sides by 8:
(8x) / 8 = (-8) / 8
x = -1
Now, let's check for extraneous solutions by substituting x=-1 back into the original equation:
4(3x + 4) = 4x + 8
4(3(-1) + 4) = 4(-1) + 8
4(-3 + 4) = -4 + 8
4(1) = 4
4 = 4
Since the equation remains true when x=-1, there are no extraneous solutions. Therefore, the solution to the equation is x = -1.
To solve the equation, we'll start by simplifying both sides of the equation:
On the left side, we distribute the 4:
4 * (3x + 4) = 12x + 16
Now we have:
12x + 16 = 4x + 8
Next, we want to isolate the variable x on one side of the equation. To do this, we'll subtract 4x from both sides:
12x - 4x + 16 = 4x - 4x + 8
Simplifying further:
8x + 16 = 8
To get rid of the constant term, we'll subtract 16 from both sides:
8x + 16 - 16 = 8 - 16
Simplifying:
8x = -8
Finally, we'll solve for x by dividing both sides by 8:
(8x)/8 = -8/8
Simplifying:
x = -1
Now, let's check for extraneous solutions by substituting x = -1 back into the original equation:
4(3x + 4) = 4x + 8
Plugging in x = -1:
4(3(-1) + 4) = 4(-1) + 8
Simplifying inside the brackets:
4(-3 + 4) = -4 + 8
Further simplification:
4(1) = 4
Left side equals right side, so the solution x = -1 is not extraneous.
Therefore, the solution to the equation is x = -1 and there are no extraneous solutions.
To solve the equation 4(3x + 4) = 4x + 8, we will follow these steps:
Step 1: Distribute the 4 on the left side of the equation:
12x + 16 = 4x + 8
Step 2: Simplify the equation by combining like terms:
12x - 4x = 8 - 16
8x = -8
Step 3: Divide both sides of the equation by 8 to isolate x:
(8x)/8 = (-8)/8
x = -1
Now, let's check for extraneous solutions by substituting x = -1 back into the original equation:
4(3(-1) + 4) = 4(-1) + 8
Simplifying both sides of the equation:
4(-3 + 4) = -4 + 8
4(1) = 4
4 = 4
Since both sides of the equation are equal, there are no extraneous solutions. The solution to the original equation is x = -1.