Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+15}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-7x } & = & -14 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-29\\\Leftrightarrow & \color{red}{-13}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-29}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{29}{13} } & & \\ & V = \left\{ \frac{29}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x } & = & -8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-22\\\Leftrightarrow & \color{red}{-6}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-8}& = & -11 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8+7x } & = & -11 \color{red}{ -7x }\color{blue}{+8+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &15x & = &-3\\\Leftrightarrow & \color{red}{15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-10}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-11x } & = & -11 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -11 \color{blue}{+10} \\\Leftrightarrow &-21x & = &-1\\\Leftrightarrow & \color{red}{-21}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-1}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{1}{21} } & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-x } & = & -2 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+14}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14+7x } & = & -10 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &11x & = &-24\\\Leftrightarrow & \color{red}{11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-24}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{11} } & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-x } & = & -2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -2 \color{blue}{+5} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+1}& = & 15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1+2x } & = & 15 \color{red}{ -2x }\color{blue}{-1+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 15 \color{blue}{-1} \\\Leftrightarrow &17x & = &14\\\Leftrightarrow & \color{red}{17}x & = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+12}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-5x } & = & 14 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-10}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-14x } & = & -1 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &-25x & = &9\\\Leftrightarrow & \color{red}{-25}x & = &9\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{9}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{25} } & & \\ & V = \left\{ \frac{-9}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9-x } & = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &12x & = &22\\\Leftrightarrow & \color{red}{12}x & = &22\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{22}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-13}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13-11x } & = & 7 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-6x & = &20\\\Leftrightarrow & \color{red}{-6}x & = &20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)