Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-11}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-7x } & = & 12 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-20x & = &23\\\Leftrightarrow & \color{red}{-20}x & = &23\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{23}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{20} } & & \\ & V = \left\{ \frac{-23}{20} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-16x & = &13\\\Leftrightarrow & \color{red}{-16}x & = &13\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{13}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{16} } & & \\ & V = \left\{ \frac{-13}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+14}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-13x } & = & -1 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-15\\\Leftrightarrow & \color{red}{-25}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-15}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-9}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+2x } & = & 5 \color{red}{ -2x }\color{blue}{+9+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &3x & = &14\\\Leftrightarrow & \color{red}{3}x & = &14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-8}& = & 3 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+9x } & = & 3 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &19x & = &11\\\Leftrightarrow & \color{red}{19}x & = &11\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{11}{19} \\\Leftrightarrow & \color{green}{ x = \frac{11}{19} } & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+15}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-x } & = & -10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-25\\\Leftrightarrow & \color{red}{-7}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-25}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{25}{7} } & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-11}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-13x } & = & 7 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & -1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-11}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-3x } & = & -1 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+6}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6+7x } & = & 9 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &15x & = &3\\\Leftrightarrow & \color{red}{15}x & = &3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3-x } & = & -14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &4x & = &-11\\\Leftrightarrow & \color{red}{4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-7}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-11x } & = & 15 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-12x & = &22\\\Leftrightarrow & \color{red}{-12}x & = &22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)