Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-2}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2-13x } & = & 12 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-x } & = & 2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-2}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2+7x } & = & -12 \color{red}{ -7x }\color{blue}{+2+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &15x & = &-10\\\Leftrightarrow & \color{red}{15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-10}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-15}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-13x } & = & -9 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &-16x & = &6\\\Leftrightarrow & \color{red}{-16}x & = &6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-11}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11-8x } & = & 9 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-9x & = &20\\\Leftrightarrow & \color{red}{-9}x & = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-x } & = & -1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4-x } & = & -2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x } & = & -4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-x } & = & 7 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+2}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-13x } & = & -6 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &-19x & = &-8\\\Leftrightarrow & \color{red}{-19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14-x } & = & -12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &10x & = &-26\\\Leftrightarrow & \color{red}{10}x & = &-26\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-26}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)