Final answer:
To simplify 2×(8x+2)=3×(2x−7), expand both sides, rearrange terms, and solve for x to find x = -2.5. Remember to always check if the solution is reasonable.
Step-by-step explanation:
To express the mathematical equation 2×(8x+2)=3×(2x−7) in a simplified form, we can follow these steps:
- Expand both sides of the equation by multiplying the factors. This gives us 16x + 4 = 6x - 21.
- Move all x terms to one side by subtracting 6x from both sides, leading to 16x - 6x + 4 = -21, which simplifies to 10x + 4 = -21.
- Next, move the constant terms to the other side by subtracting 4 from both sides, yielding 10x = -25.
- Finally, divide both sides by 10 to isolate x. The result is x = -2.5.
Remember to treat equations as sentences expressing important concepts precisely, not merely as machines for plugging in numbers.
In solving equations, we often use basic math rules: when two positive numbers multiply, their product is positive; when two negative numbers multiply, their product is also positive; but when numbers with opposite signs multiply, the result is negative. The same rules apply for division.
Once you have found an answer, always eliminate terms wherever possible to simplify the algebra and check if the answer is reasonable.