Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-10}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-9x } & = & 7 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &-17x & = &17\\\Leftrightarrow & \color{red}{-17}x & = &17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{17}{-17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+3}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-13x } & = & 11 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+15}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-7x } & = & -13 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-28\\\Leftrightarrow & \color{red}{-13}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-28}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{28}{13} } & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-4}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-9x } & = & -4 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -4 \color{blue}{+4} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-1}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-13x } & = & 2 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-16x & = &3\\\Leftrightarrow & \color{red}{-16}x & = &3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{16} } & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-12}& = & -10 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+2x } & = & -10 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-8}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-14x } & = & 15 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &-25x & = &23\\\Leftrightarrow & \color{red}{-25}x & = &23\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{23}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{25} } & & \\ & V = \left\{ \frac{-23}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-x } & = & 7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-6x & = &22\\\Leftrightarrow & \color{red}{-6}x & = &22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-11}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-9x } & = & -15 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+4}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & 15 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+4}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-11x } & = & 11 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)