Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(2x+9=-10+x\)
2. \(6x+8=-5+x\)
3. \(14x+7=-1+x\)
4. \(-2x-12=-14+x\)
5. \(15x+13=13+13x\)
6. \(8x+15=-4-13x\)
7. \(7x-1=8+6x\)
8. \(-2x+4=15+11x\)
9. \(11x-4=7-10x\)
10. \(-14x-6=-12+5x\)
11. \(5x+8=-13-7x\)
12. \(9x-4=-2+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-x } & = & -10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+8}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8-x } & = & -5 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &5x & = &-13\\\Leftrightarrow & \color{red}{5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+7}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7-x } & = & -1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x } & = & -14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+13}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-13x } & = & 13 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &2x & = &0\\\Leftrightarrow & \color{red}{2}x & = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+15}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15+13x } & = & -4 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &21x & = &-19\\\Leftrightarrow & \color{red}{21}x & = &-19\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-19}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{21} } & & \\ & V = \left\{ \frac{-19}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-1}& = & 8 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1-6x } & = & 8 \color{red}{ +6x }\color{blue}{+1-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+4}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-11x } & = & 15 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-4}& = & 7 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4+10x } & = & 7 \color{red}{ -10x }\color{blue}{+4+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &21x & = &11\\\Leftrightarrow & \color{red}{21}x & = &11\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{11}{21} \\\Leftrightarrow & \color{green}{ x = \frac{11}{21} } & & \\ & V = \left\{ \frac{11}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-6}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-5x } & = & -12 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-19x & = &-6\\\Leftrightarrow & \color{red}{-19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-6}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+8}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8+7x } & = & -13 \color{red}{ -7x }\color{blue}{-8+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &12x & = &-21\\\Leftrightarrow & \color{red}{12}x & = &-21\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-21}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4-x } & = & -2 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &8x & = &2\\\Leftrightarrow & \color{red}{8}x & = &2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)