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
If \( x+1=3 \), what is the value of \( 2(x+1) \) ?
原库参考解析
一元一次方程与代数求值挑战
\( 1.5c+3d=108 \)
The given equation describes the relationship between the number of cats, c, and the number of dogs, d, that can be cared for at a pet care business during a week. If the business cares for 36 dogs during a week, how many cats can it care for during this week?
原库参考解析
一元一次方程与代数求值挑战
\( 6\left(t+7\right)-8\left(t+7\right)=38 \)
What value of t 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
\( b-20=\frac{x}{y} \)
The given equation relates the positive numbers b, x , and y . Which equation correctly expresses x in terms of b and y ?
原库参考解析
一元一次方程与代数求值进阶
All the sidewalk paving stones in a neighborhood are rectangular. The length of each of these paving stones is 41 centimeters greater than the width. Which equation gives the area A, in square centimeters, of a sidewalk paving stone in terms of the width w , in centimeters, of that paving stone?
原库参考解析
一元一次方程与代数求值进阶
During hibernation, American black bears do not eat or replenish calories. A certain black bear weighed 338 pounds when entering hibernation and lost weight at a rate of 0.7 pound per day. At this rate, how many days after entering hibernation did the black bear weigh 310 pounds?
原库参考解析
一元一次方程与代数求值挑战
If \( \frac{x+5}{3}=\frac{x+5}{12} \), the value of \( x+5 \) is between which of the following pairs of values?
原库参考解析
一元一次方程与代数求值挑战
\( 32x+81y=290 \)
The given equation represents the volume of mulch x, in cubic feet, and the volume of soil y, in cubic feet, in a mixture of mulch and soil that weighs 290 pounds. If the volume of soil in the mixture is 2 cubic feet, what is the volume of mulch in the mixture, in cubic feet?
原库参考解析
一元一次方程与代数求值进阶
If \( \frac{x}{y}=64 \) and \( \frac{cx}{4y}=64 \), what is the value of c?
原库参考解析
一元一次方程与代数求值进阶
If \( 7\left(6-9x\right)+4=6\left(6-9x\right)+19 \), what is the value of \( 6−9x \)?
原库参考解析
一元一次方程与代数求值进阶
\( \frac{j}{5}=k+9m \)
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
If \( 5+x=2 \), what is the value of \( −15−3x^2 \) ?
原库参考解析
