Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+12}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12+13x } & = & 10 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &22x & = &-2\\\Leftrightarrow & \color{red}{22}x & = &-2\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-2}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & 12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &-16x & = &27\\\Leftrightarrow & \color{red}{-16}x & = &27\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{27}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{16} } & & \\ & V = \left\{ \frac{-27}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-4}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4-7x } & = & -2 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-1}& = & -9 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+7x } & = & -9 \color{red}{ -7x }\color{blue}{+1+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &12x & = &-8\\\Leftrightarrow & \color{red}{12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-8}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+14}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14-11x } & = & 10 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-5}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5-5x } & = & 15 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &x & = &20\\\Leftrightarrow & \color{red}{}x & = &20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 20 \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+11}& = & -5 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-8x } & = & -5 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &-23x & = &-16\\\Leftrightarrow & \color{red}{-23}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-16}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{16}{23} } & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-7}& = & 6 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-4x } & = & 6 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &-19x & = &13\\\Leftrightarrow & \color{red}{-19}x & = &13\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{13}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{19} } & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-8}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x } & = & 9 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &-3x & = &17\\\Leftrightarrow & \color{red}{-3}x & = &17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-9}& = & 3 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-12x } & = & 3 \color{red}{ +12x }\color{blue}{+9-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-10}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-13x } & = & -7 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-25x & = &3\\\Leftrightarrow & \color{red}{-25}x & = &3\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{3}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{25} } & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)