Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+8}& = & 4 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8+10x } & = & 4 \color{red}{ -10x }\color{blue}{-8+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &9x & = &-4\\\Leftrightarrow & \color{red}{9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+14}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14+7x } & = & -3 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &19x & = &-17\\\Leftrightarrow & \color{red}{19}x & = &-17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+2}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2-4x } & = & -1 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-3}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-8x } & = & -15 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-15}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-13x } & = & 6 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &-x & = &21\\\Leftrightarrow & \color{red}{-}x & = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-7}& = & 4 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7+4x } & = & 4 \color{red}{ -4x }\color{blue}{+7+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 4 \color{blue}{+7} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-x } & = & -7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-16x & = &-11\\\Leftrightarrow & \color{red}{-16}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{16} } & & \\ & V = \left\{ \frac{11}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15-x } & = & -11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x } & = & 10 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &-16x & = &16\\\Leftrightarrow & \color{red}{-16}x & = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & -6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-x } & = & -12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-26\\\Leftrightarrow & \color{red}{-3}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-26}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{26}{3} } & & \\ & V = \left\{ \frac{26}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-7}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-x } & = & 13 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &-10x & = &20\\\Leftrightarrow & \color{red}{-10}x & = &20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{20}{-10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)