一、根据 $4x + 3 = 39$ 的解方程过程填一填。
$\begin{aligned}4x + 3 &= 39\\解:4x + 3 - 3 &= 39 - 3\\4x &= 36\\4x ÷ 4 &= 36 ÷ 4\\x &= 9\end{aligned} $
在解方程 $4x + 3 = 39$ 时,因为 $x$ 未知,可以把( )看作一个整体,先把等式两边同时( ),此时原方程简化为( )。这样原来复杂的方程就转化成简单的方程了。
$\begin{aligned}4x + 3 &= 39\\解:4x + 3 - 3 &= 39 - 3\\4x &= 36\\4x ÷ 4 &= 36 ÷ 4\\x &= 9\end{aligned} $
在解方程 $4x + 3 = 39$ 时,因为 $x$ 未知,可以把( )看作一个整体,先把等式两边同时( ),此时原方程简化为( )。这样原来复杂的方程就转化成简单的方程了。
答案
4x + 3 减 3 4x = 36
二、解方程(带 ※ 的请验算)。
$3 + 7x = 24$ $\quad\quad\quad$ $12 - 2x = 5$ $\quad\quad\quad$ $5x - 10 = 200$
$1.5x + 2.5 = 20.5$ $\quad\quad\quad$ ※$1.8x - 12.4 = 23.6$
$3 + 7x = 24$ $\quad\quad\quad$ $12 - 2x = 5$ $\quad\quad\quad$ $5x - 10 = 200$
$1.5x + 2.5 = 20.5$ $\quad\quad\quad$ ※$1.8x - 12.4 = 23.6$
答案
x = 3 x = 3.5 x = 42 x = 12 x = 20(验算略)
解析
解:$3 + 7x = 24$
$7x = 24 - 3$
$7x = 21$
$x = 3$
解:$12 - 2x = 5$
$-2x = 5 - 12$
$-2x = -7$
$x = 3.5$
解:$5x - 10 = 200$
$5x = 200 + 10$
$5x = 210$
$x = 42$
解:$1.5x + 2.5 = 20.5$
$1.5x = 20.5 - 2.5$
$1.5x = 18$
$x = 12$
解:$1.8x - 12.4 = 23.6$
$1.8x = 23.6 + 12.4$
$1.8x = 36$
$x = 20$
验算:将$x = 20$代入原方程左边,$1.8×20 - 12.4 = 36 - 12.4 = 23.6$,右边$= 23.6$,左边$=$右边,所以$x = 20$是原方程的解。
$7x = 24 - 3$
$7x = 21$
$x = 3$
解:$12 - 2x = 5$
$-2x = 5 - 12$
$-2x = -7$
$x = 3.5$
解:$5x - 10 = 200$
$5x = 200 + 10$
$5x = 210$
$x = 42$
解:$1.5x + 2.5 = 20.5$
$1.5x = 20.5 - 2.5$
$1.5x = 18$
$x = 12$
解:$1.8x - 12.4 = 23.6$
$1.8x = 23.6 + 12.4$
$1.8x = 36$
$x = 20$
验算:将$x = 20$代入原方程左边,$1.8×20 - 12.4 = 36 - 12.4 = 23.6$,右边$= 23.6$,左边$=$右边,所以$x = 20$是原方程的解。
三、看图列方程,并求出方程的解。
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答案
1. 3x + 15 = 17.4 x = 0.8 2. 4x - 50 = 430 x = 120 3. 30×2 + 2x = 158 x = 49 4. 2x + 63 = 105 x = 21
解析
1. 3x + 15 = 17.4
3x = 17.4 - 15
3x = 2.4
x = 0.8
2. 4x - 50 = 430
4x = 430 + 50
4x = 480
x = 120
3. 30×2 + 2x = 158
60 + 2x = 158
2x = 158 - 60
2x = 98
x = 49
4. 2x + 63 = 105
2x = 105 - 63
2x = 42
x = 21
3x = 17.4 - 15
3x = 2.4
x = 0.8
2. 4x - 50 = 430
4x = 430 + 50
4x = 480
x = 120
3. 30×2 + 2x = 158
60 + 2x = 158
2x = 158 - 60
2x = 98
x = 49
4. 2x + 63 = 105
2x = 105 - 63
2x = 42
x = 21
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