Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+9}& = & 1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9+6x } & = & 1 \color{red}{ -6x }\color{blue}{-9+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &19x & = &-8\\\Leftrightarrow & \color{red}{19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-x } & = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &-10x & = &21\\\Leftrightarrow & \color{red}{-10}x & = &21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{10} } & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-4}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4+11x } & = & -8 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &17x & = &-4\\\Leftrightarrow & \color{red}{17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-15}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x } & = & -4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-x } & = & 11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & -15 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-8}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8-x } & = & 6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &2x & = &14\\\Leftrightarrow & \color{red}{2}x & = &14\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{14}{2} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-3}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-13x } & = & -8 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-14}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-11x } & = & 7 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &-18x & = &21\\\Leftrightarrow & \color{red}{-18}x & = &21\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{21}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-14}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14+13x } & = & -13 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &27x & = &1\\\Leftrightarrow & \color{red}{27}x & = &1\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{1}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{27} } & & \\ & V = \left\{ \frac{1}{27} \right\} & \\\end{align}\)