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进阶
11x = 96 - x
What value of x is the solution to the given equation?
原库参考解析
一元一次方程与代数求值进阶
v =\( -\frac{w}{150x} \)
The given equation relates the distinct positive numbers v, w, and x. Which equation correctly expresses w in terms of v and x ?
原库参考解析
一元一次方程与代数求值进阶
\( \frac{j}{8}=k+11m \)
The given equation relates the distinct positive numbers j, k, and m. Which equation correctly expresses j in terms of k and m?
原库参考解析
一元一次方程与代数求值进阶
A batch of smoothies consists of 4 cups of milk and 2 bananas and has 1,172 milligrams (mg) of calcium. There is 290 mg of calcium in 1 cup of milk. How much calcium, in mg, is in 1 banana?
原库参考解析
一元一次方程与代数求值挑战
A proposal for a construction project was included on a city election ballot, A TV news report stated that 8 times as many people voted in favor of the proposal as people who voted against it. An internet article reported that 31,500 more people voted in favor of the proposal than voted against it, Based on these data, how many people voted against the proposal?
原库参考解析
一元一次方程与代数求值挑战
Which expression is equivalent to 80y+ 70y?
原库参考解析
一元一次方程与代数求值挑战
If 5(x+3)= 25, what is the value of x+ 3?
原库参考解析
一元一次方程与代数求值进阶
The equation 8p+8w = 720 represents the number of purple tiles, p. and the number of white tiles, w, a designer needs to cover a 720-square-inch section of a wall.The designer needs 34 purple tiles for the wall.How many white tiles does she need?
原库参考解析
一元一次方程与代数求值进阶
\( ak=\frac{b}{10}\left(9+m\right) \)
The given equation relates the positive variables a,b. k, and m. Which equation correctly expresses m in terms of a.b,and k?
原库参考解析
一元一次方程与代数求值进阶
y =2x + 43
which table gives three values of x and their corresponding values of y for the given equation?
原库参考解析
一元一次方程与代数求值挑战
A proposal for a construction project was included on a city election ballot. A TV news report stated that 8 times as many people voted in favor of the proposal as people who voted against it. An internet article reported that 31,500 more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?
原库参考解析
一元一次方程与代数求值挑战
Which expression is equivalent to 80y + 70y ?
原库参考解析
