Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-1}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1+7x } & = & 6 \color{red}{ -7x }\color{blue}{+1+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &19x & = &7\\\Leftrightarrow & \color{red}{19}x & = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-13}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-7x } & = & 9 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &-17x & = &22\\\Leftrightarrow & \color{red}{-17}x & = &22\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{22}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{17} } & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-x } & = & -7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &11x & = &4\\\Leftrightarrow & \color{red}{11}x & = &4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-x } & = & -6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & -10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &x & = &24\\\Leftrightarrow & \color{red}{}x & = &24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 24 \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+7}& = & 8 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7-10x } & = & 8 \color{red}{ +10x }\color{blue}{-7-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & 8 \color{blue}{-7} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-2}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x } & = & -15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -15 \color{blue}{+2} \\\Leftrightarrow &-5x & = &-13\\\Leftrightarrow & \color{red}{-5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-x } & = & 6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-11}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-11x } & = & 9 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-16x & = &20\\\Leftrightarrow & \color{red}{-16}x & = &20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-x } & = & 1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 1 \color{blue}{+11} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-2}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2-5x } & = & 12 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &6x & = &14\\\Leftrightarrow & \color{red}{6}x & = &14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)