If X/5 + 6 = -14, then X = ? Show work.
If X/5 + 6 = -14, then X = ? Show work.
The Correct Answer and Explanation is:
We are given the equation:X5+6=−14\frac{X}{5} + 6 = -145X+6=−14
Step-by-step solution:
Step 1: Subtract 6 from both sides to isolate the term with XX5+6−6=−14−6\frac{X}{5} + 6 – 6 = -14 – 65X+6−6=−14−6X5=−20\frac{X}{5} = -205X=−20
Step 2: Multiply both sides of the equation by 5 to solve for X5⋅X5=−20⋅55 \cdot \frac{X}{5} = -20 \cdot 55⋅5X=−20⋅5X=−100X = -100X=−100
✅ Final Answer:
X=−100X = -100X=−100
Explanation
Solving equations like X5+6=−14\frac{X}{5} + 6 = -145X+6=−14 involves the use of basic algebraic principles to isolate the variable. The goal is to find the value of X that makes the equation true. This particular equation is a linear equation, which means it graphs as a straight line and the variable X is raised to the first power.
The first step in solving X5+6=−14\frac{X}{5} + 6 = -145X+6=−14 is to eliminate the constant term on the left side of the equation. Since there is a +6 being added to X5\frac{X}{5}5X, we perform the opposite operation—subtracting 6 from both sides. This gives us X5=−20\frac{X}{5} = -205X=−20.
Next, we want to get rid of the fraction. Since X is divided by 5, we do the opposite and multiply both sides by 5. This cancels out the denominator on the left side, and we are left with:X=−100X = -100X=−100
This is our solution. We can check our work by substituting -100 back into the original equation:−1005+6=−20+6=−14\frac{-100}{5} + 6 = -20 + 6 = -145−100+6=−20+6=−14
Since both sides equal -14, the solution is verified.
This problem demonstrates important skills in algebra: performing inverse operations (like subtracting 6 or multiplying by 5) and keeping the equation balanced by applying the same operation to both sides. Understanding these steps helps build a strong foundation for more complex equations and problem-solving in math.
