Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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