这部分需要会什么？
- 熟练去括号、通分、移项和合并同类项
- 区分求未知数与求一个代数式的值
- 识别无解、唯一解和恒等式
核心概念与公式
一元一次方程整理后可以写成 \(ax+b=c\)。当 \(a\ne0\) 时，\(x=(c-b)/a\)。等式两边做同一种合法运算，解保持不变；除法的除数不能为零。
若未知数项消去，留下真等式（如 \(0=0\)），则原允许范围内所有数都是解；留下假等式（如 \(0=5\)），则无解。题目若只问 \(2x+3\)，可以把它当成整体，不必一定先求 \(x\)。
做题时怎样使用
- 先看题目最终要求什么，并标出分母或其他取值限制
- 去括号、通分，整理未知数项与常数项；有参数时先判断能否除以它
- 得到答案后代回原式，尤其检查负号和括号
容易混淆的地方
\(-(x-3)=-x+3\)，不是 \(-x-3\)。若等式中某个系数可能为零，直接除以它会漏掉特殊情况。
用一个例题串起方法
知识点教学例题已知 \(5(2x-1)=3x+16\)，求 \(2x+3\)。
展开解题思路 ＋
展开得 \(10x-5=3x+16\)，于是 \(7x=21\)，\(x=3\)。题目要求的是 \(2x+3=9\)，不能把中间结果 3 当作最终答案。
本知识点题库
先独立作答，再查看答案与解析。
一元一次方程与代数求值挑战
\( 4xy+5xt-17yt=0 \)
In the given equation, x and y are positive and x < y. Which equation correctly expresses t in terms of x and y?
In the given equation, x and y are positive and x < y. Which equation correctly expresses t in terms of x and y?
参考答案
一元一次方程与代数求值挑战
If \( 4(2t-5)+t=40+7t \), what is the value of 2t?
参考答案
一元一次方程与代数求值基础
\( 3j+14k=m \)
The given equation relates the numbers j, k, and m. Which equation correctly expresses k in terms of j and m?
The given equation relates the numbers j, k, and m. Which equation correctly expresses k in terms of j and m?
参考答案
一元一次方程与代数求值基础
\( 2.7x=270 \)
What value of x is the solution to the given equation?
What value of x is the solution to the given equation?
参考答案
一元一次方程与代数求值进阶
The equation \( x+y=1,440 \) represents the number of minutes of daylight (between sunrise and sunset), x, and the number of minutes of non-daylight, y, on a particular day in Grand Rapids, Michigan. If this day has 740 minutes of daylight, how many minutes of non-daylight does it have?
参考答案
一元一次方程与代数求值进阶
If \( \frac{x}{8}=5 \), what is the value of \( \frac{8}{x} \)?
参考答案
一元一次方程与代数求值进阶
If \( 6-24x=3 \), what is the value of \( 1−4x \)?
参考答案
一元一次方程与代数求值基础
\( \frac{7}{x+2}=\frac{7}{13} \)
What value of x is the solution to the given equation?
What value of x is the solution to the given equation?
参考答案
一元一次方程与代数求值基础
\( \frac{r}{31}=s+t \)
The given equation relates the quantities r, s, and t. Which equation correctly expresses r in terms of s and t?
The given equation relates the quantities r, s, and t. Which equation correctly expresses r in terms of s and t?
参考答案
一元一次方程与代数求值基础
Which expression is equivalent to \( 7x^3+2+8 \)?
参考答案
一元一次方程与代数求值基础
\( 2.6x=2,600 \)
What value of x is the solution to the given equation?
What value of x is the solution to the given equation?
参考答案
一元一次方程与代数求值挑战
\( P=N(57-C) \)
The given equation relates the positive numbers P, N, and C. Which equation correctly expresses C in terms of P and N?
The given equation relates the positive numbers P, N, and C. Which equation correctly expresses C in terms of P and N?
参考答案
