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
\( x+y=53 \)
The given equation relates the total number of marble queen pothos stems, x, and the total number of snow queen pothos stems, y, a plant nursery propagates to create pothos plants. If 13 snow queen pothos stems are propagated, how many marble queen pothos stems are propagated?
原库参考解析
一元一次方程与代数求值进阶
\( 18qrt-2qrs+10rst=0 \)
In the given equation, q, r, s, and t are positive, and \( \frac{q}{t} \) is greater than 5. Which expression is equivalent to s?
原库参考解析
一元一次方程与代数求值基础
\( 5a=\frac{4b^2}{a}-20a \)
The given equation relates the positive variables a and b. Which equation correctly expresses a in terms of b?
原库参考解析
一元一次方程与代数求值基础
A chemist combines 25 grams of compound A, 35 grams of compound B, and x grams of compound C. The resulting mixture has a mass of 125 grams. What is the value of x?
原库参考解析
一元一次方程与代数求值基础
If \( 5c=15 \), what is the value of \( 5c−8 \)?
原库参考解析
一元一次方程与代数求值进阶
\( b^2+4c=7d \)
The given equation relates the real numbers b, c, and d, where \( d>\frac{4}{7}c \). Which equation correctly expresses b in terms of c and d ?
原库参考解析
一元一次方程与代数求值进阶
If \( 9x+4=67 \),what is the value of \( 90x+40 \)?
原库参考解析
一元一次方程与代数求值进阶
If\( 6x-8=4 \), what is the value of \( 6x+8 \)?
原库参考解析
一元一次方程与代数求值挑战
\( b^2+5c=6d \)
The given equation relates the real numbers b, c, and d and, where \( d>\frac{5}{6}c \) . Which equation correctly expresses b in terms of c and d ?
原库参考解析
一元一次方程与代数求值进阶
What value of p is the solution to the equation \( 4p-5p=14 \)?
原库参考解析
一元一次方程与代数求值进阶
If \( 3-2x=42 \), what is the value of \( \frac{1}{6}(3-2x) \)?
原库参考解析
一元一次方程与代数求值挑战
\( 0.10x+0.20y=0.17(x+y) \)
The equation gives a volume x, in gallons, of a 10% saltwater solution that could be mixed with a volume y, in gallons, of a 20% saltwater solution to produce a 17% saltwater solution. According to this equation, what volume, in gallons, of the 20% saltwater solution could be mixed with 75.0 gallons of the 10% saltwater solution to produce a 17% saltwater solution? (Assume that the volume of the mixture is the sum of the volumes of the two solutions before they were mixed.)
原库参考解析
