Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &6x & = &24\\\Leftrightarrow & \color{red}{6}x & = &24\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{24}{6} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+13}& = & 4 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+10x } & = & 4 \color{red}{ -10x }\color{blue}{-13+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &21x & = &-9\\\Leftrightarrow & \color{red}{21}x & = &-9\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-9}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+3}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-9x } & = & -14 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -14 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-17\\\Leftrightarrow & \color{red}{-5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+10}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10-5x } & = & 12 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &7x & = &2\\\Leftrightarrow & \color{red}{7}x & = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+14}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-13x } & = & -2 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-16\\\Leftrightarrow & \color{red}{-16}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-16}{-16} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+5}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-13x } & = & -4 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -4 \color{blue}{-5} \\\Leftrightarrow &-25x & = &-9\\\Leftrightarrow & \color{red}{-25}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-9}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{9}{25} } & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-8}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-x } & = & 12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &3x & = &20\\\Leftrightarrow & \color{red}{3}x & = &20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+2}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2+2x } & = & -7 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-8}& = & 9 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8+6x } & = & 9 \color{red}{ -6x }\color{blue}{+8+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &19x & = &17\\\Leftrightarrow & \color{red}{19}x & = &17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{17}{19} } & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-x } & = & 15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-8}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-10x } & = & -9 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)