Solving the Equation 6x-5×3-287x Step-by-Step

Introduction to Equations: Equations are a fundamental part of algebra, allowing us to express and solve relationships between variables. This article will guide you through solving a linear equation, 6x-5×3-287x, step by step. We will explore the principles, the solution process, and verification methods.

Understanding the Equation

The given equation is 6x-5×3-287x. Let's break down what each term means and how to approach solving it.

Given Equation

Original Equation: 6x-5×3-287x

Simplifying the Equation

Combine like terms: First, simplify the left side of the equation. Notice that -5×3 is a multiplication, resulting in -15, and then we subtract 28. This simplifies to: Simplified Equation: 6x-15-287x Add like terms: Combine the constants on the left side: Further Simplification: 6x-437x

Rearranging the Equation to Isolate x

Move the term with x to one side: To isolate x, move 6x to the right side of the equation with a change of sign: Equation with x isolated: 7x-6x-43 Simplify the left side: 7x-6x reduces to x: Final Simplification: x-43

However, it seems there was an overlook in the simplification process. Let's review the correct steps again:

Correct Approach to Solving the Equation

Start with the original equation: 6x-5×3-287x Simplify the left side: -5×3 -15, then -15-28 -43: Write the simplified equation: 6x-437x Rearrange to isolate x: Subtract 6x from both sides: Resulting equation: -437x-6x x Further simplification: -43x Final Answer: x-43

Verification

To verify our solution, substitute x-43 into the original equation:

Left-hand side (LHS): 6(-43) - 5×3 - 28 -258 - 15 - 28 -291 Right-hand side (RHS): 7(-43) -301 Conclusion: Since LHS is not equal to RHS, the previous simplification or solving steps may have an error. Let's correct it: Correct steps: 6x-15-287x, then 6x-7x-15-28, -x-43, x43

Conclusion

The correct solution to the equation 6x-5×3-287x is x43. Always recheck your steps and verify the solution in the original equation to ensure accuracy.

Keywords

Equation solving, linear equation, algebraic equation