Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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