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 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 Des Moines, Iowa. If this day has 840 minutes of daylight, how many minutes of non-daylight does it have?
原库参考解析
一元一次方程与代数求值进阶
If \( \frac{x}{9}=5 \), what is the value of \( \frac{9}{x} \) ?
原库参考解析
一元一次方程与代数求值挑战
If \( \left(\frac{1}{2}x-\frac{41}{2}\right)^2-64=0 \), what is the value of \( (x-41)^2 \) ?
原库参考解析
一元一次方程与代数求值挑战
Javier deposits $45 in a savings account at the end of each week. At the beginning of the 1st week of a year there was $900 in that savings account. How much money, in dollars, will be in the account at the end of the 4th week of the year?
原库参考解析
一元一次方程与代数求值进阶
\( a=\frac{3}{11}b+6 \)
The given equation relates the positive numbers a and b. Which equation correctly expresses b in terms of a?
原库参考解析
一元一次方程与代数求值进阶
If 9x+4=32, what is the value of 3(9x+4)?
原库参考解析
一元一次方程与代数求值挑战
The equation \( h=\frac{9(v−273.15)}{5}+32 \) gives the corresponding temperature h, in degrees Fahrenheit, of any substance that has a temperature of v kelvins, where v>0. If a substance has a temperature of 557.33 degrees Fahrenheit, what is the corresponding temperature, in kelvins, of this substance?
原库参考解析
一元一次方程与代数求值挑战
If x-2=3, what is the value of 3(x-2)?
原库参考解析
一元一次方程与代数求值挑战
If a=3k+5r and b=9k-12r+6, which expression is equivalent to a-b?
原库参考解析
一元一次方程与代数求值进阶
\( b-19=\frac{x}{y} \)
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
The length of a rectangle is 35 centimeters greater than its width. Which equation gives the area A, in square centimeters, of the rectangle in terms of the width w, in centimeters, of the rectangle?
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 515 pounds when entering hibernation and lost weight at a rate of 0.5 pound per day. At this rate, how many days after entering hibernation did the black bear weigh 490 pounds?
原库参考解析
