7x – 6= 3x – 26
Solve the equation above for x. Which of the following is the value for x?
A.
-5
B.
6
C.
5
D.
-8
The correct answer and Explanation is :
To solve the equation (7x – 6 = 3x – 26) for (x), follow these steps:
- Combine like terms: First, get all the (x) terms on one side of the equation and the constant terms on the other side. To do this, subtract (3x) from both sides of the equation: [
7x – 6 – 3x = 3x – 26 – 3x
] Simplifying this, we get: [
4x – 6 = -26
] - Isolate the (x) term: Next, get rid of the constant term on the left side by adding 6 to both sides of the equation: [
4x – 6 + 6 = -26 + 6
] Simplifying this, we get: [
4x = -20
] - Solve for (x): Finally, divide both sides of the equation by 4 to solve for (x): [
\frac{4x}{4} = \frac{-20}{4}
] Simplifying this, we get: [
x = -5
]
So, the value of (x) is (-5).
Explanation
To solve an equation like (7x – 6 = 3x – 26), the goal is to isolate (x) on one side of the equation. This process involves moving all (x) terms to one side and constant terms to the other side. By performing algebraic operations such as addition or subtraction and then dividing or multiplying, we can find the value of (x) that satisfies the equation.
In this case, subtracting (3x) from both sides simplifies the equation to (4x – 6 = -26). Adding 6 to both sides further simplifies it to (4x = -20). Dividing both sides by 4 yields (x = -5). Each step helps to progressively simplify the equation until (x) is isolated and solved for.
Thus, the correct answer is:
A. -5