Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+5}& = & -9 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5+14x } & = & -9 \color{red}{ -14x }\color{blue}{-5+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &19x & = &-14\\\Leftrightarrow & \color{red}{19}x & = &-14\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-14}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+7}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7-11x } & = & 3 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-4}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4+13x } & = & 9 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & -7x \color{blue}{+13x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &6x & = &13\\\Leftrightarrow & \color{red}{6}x & = &13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-9}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-4x } & = & 8 \color{red}{ +4x }\color{blue}{+9-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &7x & = &17\\\Leftrightarrow & \color{red}{7}x & = &17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+7}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7+11x } & = & -9 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & -14x \color{blue}{+11x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &-3x & = &-16\\\Leftrightarrow & \color{red}{-3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-6}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6-x } & = & -4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &6x & = &2\\\Leftrightarrow & \color{red}{6}x & = &2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+15}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-13x } & = & -7 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-22\\\Leftrightarrow & \color{red}{-15}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-22}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{22}{15} } & & \\ & V = \left\{ \frac{22}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+9}& = & -15 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9-14x } & = & -15 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &x & = &-24\\\Leftrightarrow & \color{red}{}x & = &-24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -24 \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+10}& = & 8 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10+7x } & = & 8 \color{red}{ -7x }\color{blue}{-10+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & 8 \color{blue}{-10} \\\Leftrightarrow &6x & = &-2\\\Leftrightarrow & \color{red}{6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+3}& = & -12 \color{red}{ -9x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3+9x } & = & -12 \color{red}{ -9x }\color{blue}{-3+9x } \\\Leftrightarrow & -14x \color{blue}{+9x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+11}& = & 2 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11-6x } & = & 2 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-13}& = & 8 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13-10x } & = & 8 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & 8 \color{blue}{+13} \\\Leftrightarrow &-9x & = &21\\\Leftrightarrow & \color{red}{-9}x & = &21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)