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
The kinetic energy K, in joules, of an object is given by the formula \( K=\frac{1}{2}mv^2 \), where m is the mass of the object, in kilograms, and v is the velocity of the object, in meters per second. If the kinetic energy of a certain object can be found by using the formula \( K=34v^2 \), what is the mass of the object, in kilograms?
原库参考解析
一元一次方程与代数求值进阶
\( 11x+50=160 \)
Which equation has the same solution as the given equation?
原库参考解析
一元一次方程与代数求值进阶
Which expression is equivalent to\( \left(3c+9\right)-\left(4c^3-5\right) \)?
原库参考解析
一元一次方程与代数求值进阶
Which expression is equivalent to \( \left(5x^3-3x+8\right)-\left(9x^6+5x-3\right) \)?
原库参考解析
一元一次方程与代数求值挑战
What is an equation of the graph shown?
原库参考解析
一元一次方程与代数求值进阶
\( 5\left(x-4\right)+6=3\left(x-2\right)+22 \)
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
Which expression is equivalent to \( 30y+80y \)?
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 \( 8p-9p=8 \)?
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 90.0 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
一元一次方程与代数求值挑战
\( \frac{1}{4xy}+xyz=\frac{1}{3y} \)
In the given equation x, y and z are positive numbers. Which expression is equivalent to y ?
原库参考解析
一元一次方程与代数求值挑战
If \( 2(5x)=6 \), what is the value of \( 5x \)?
原库参考解析
一元一次方程与代数求值进阶
If \( \frac{x}{y}=4 \) and \( \frac{24x}{ny}=4 \), what is the value of n?
原库参考解析
