Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-9}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+2x } & = & 1 \color{red}{ -2x }\color{blue}{+9+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &17x & = &10\\\Leftrightarrow & \color{red}{17}x & = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+7}& = & 5 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7+6x } & = & 5 \color{red}{ -6x }\color{blue}{-7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &19x & = &-2\\\Leftrightarrow & \color{red}{19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-x } & = & 1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 1 \color{blue}{+11} \\\Leftrightarrow &-8x & = &12\\\Leftrightarrow & \color{red}{-8}x & = &12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & -5 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -5 \color{blue}{+10} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+7}& = & 8 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-12x } & = & 8 \color{red}{ +12x }\color{blue}{-7-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 8 \color{blue}{-7} \\\Leftrightarrow &-23x & = &1\\\Leftrightarrow & \color{red}{-23}x & = &1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+10}& = & -1 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+14x } & = & -1 \color{red}{ -14x }\color{blue}{-10+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &15x & = &-11\\\Leftrightarrow & \color{red}{15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-11}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-9}& = & 7 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9+3x } & = & 7 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &7x & = &16\\\Leftrightarrow & \color{red}{7}x & = &16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+3}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-9x } & = & -5 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+6}& = & -15 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6+5x } & = & -15 \color{red}{ -5x }\color{blue}{-6+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -15 \color{blue}{-6} \\\Leftrightarrow &8x & = &-21\\\Leftrightarrow & \color{red}{8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-21}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+3}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3-5x } & = & -14 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & -14 \color{blue}{-3} \\\Leftrightarrow &-6x & = &-17\\\Leftrightarrow & \color{red}{-6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-11}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-13x } & = & -8 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &-19x & = &3\\\Leftrightarrow & \color{red}{-19}x & = &3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+12}& = & -9 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+13x } & = & -9 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &20x & = &-21\\\Leftrightarrow & \color{red}{20}x & = &-21\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-21}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{20} } & & \\ & V = \left\{ \frac{-21}{20} \right\} & \\\end{align}\)