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# 数学演習 中学校1年生/文字の式/解答

## 文字式の表し方

1. ${\displaystyle 2a}$
2. ${\displaystyle 5ax}$
3. ${\displaystyle -x+y}$
4. ${\displaystyle a^{3}b^{2}}$
5. ${\displaystyle {\frac {a}{7}}}$　または　${\displaystyle {\frac {1}{7}}a}$
6. ${\displaystyle {\frac {x+y}{5}}}$
7. ${\displaystyle x+{\frac {y}{5}}}$

## 代入と式の値

1. ${\displaystyle 5x+7=5\times (-3)+7=-15+7=-8}$
2. ${\displaystyle 4-2x=4-2\times (-3)=4-(-6)=10}$
3. ${\displaystyle -{\frac {12}{x}}=-{\frac {12}{-3}}=-(-4)=4}$
4. ${\displaystyle x^{2}=(-3)^{2}=9}$
5. ${\displaystyle -x^{2}=-(-3)^{2}=-9}$

## 1次式の加減

1. ${\displaystyle 5x+3x=(5+3)x=8x}$
2. ${\displaystyle 5a-4a=(5-4)a=a}$
3. ${\displaystyle 7a+3-5a-6=7a-5a+3-6=(7-5)a+(3-6)=2a-3}$
4. ${\displaystyle 3x-2-x+9=3x+x-2+9=(3-1)x+(-2+9)=2x+7}$
5. ${\displaystyle (3a+2)+(6a-5)=3a+2+6a-5=9a-3}$
6. ${\displaystyle (5x-9)+(-3x+9)=5x-9-3x+9=2x}$
7. ${\displaystyle {\begin{matrix}(5a-3)-(3a+2)&=&(5a-3)+(-3a-2)\\\ &=&5a-3-3a-2&=&2a-5\end{matrix}}}$
8. ${\displaystyle {\begin{matrix}(a-7)-(2a+7)&=&(a-7)+(-2a-7)\\\ &=&a-7-2a-7&=&-a-14\end{matrix}}}$

## 1次式と数の乗除

1. ${\displaystyle 3x\times 4=3\times x\times 4=3\times 4\times x=12x}$
2. ${\displaystyle {\frac {2}{5}}a\times (-10)={\frac {2}{5}}\times a\times (-10)={\frac {2}{5}}\times (-10)\times a=-4a}$
3. ${\displaystyle 3(x+6)=3\times x+3\times 6=3x+18}$
4. ${\displaystyle -4(2x-5)=(-4)\times 2x+(-4)\times (-5)=-8x+20}$
5. ${\displaystyle {\frac {5a-3}{7}}\times 14={\frac {(5a-3)\times 14}{7}}=2(5a-3)=10a-6}$
6. ${\displaystyle 12x\div 6=12x\times {\frac {1}{6}}=2x}$
7. ${\displaystyle 9a\div {\frac {3}{4}}=9a\times {\frac {4}{3}}=12a}$
8. ${\displaystyle (18a-15)\div 3=(18a-15)\times {\frac {1}{3}}=6a-5}$
9. ${\displaystyle (24a-8)\div (-8)=(24a-8)\times \left(-{\frac {1}{8}}\right)=-3a+1}$
10. ${\displaystyle 6(a+2)+5(2a-3)=6a+12+10a-15=16a-3}$
11. ${\displaystyle 2(x+3)-3(2x-1)=2x+6-6x+3=-4x+9}$