Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-14}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-9x } & = & -9 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+14}& = & -4 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14-10x } & = & -4 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &3x & = &-18\\\Leftrightarrow & \color{red}{3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-18}{3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & -14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-25\\\Leftrightarrow & \color{red}{-11}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-25}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{25}{11} } & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-x } & = & 6 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+7}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-9x } & = & -13 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &-17x & = &-20\\\Leftrightarrow & \color{red}{-17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-20}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{20}{17} } & & \\ & V = \left\{ \frac{20}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-6}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6+5x } & = & 8 \color{red}{ -5x }\color{blue}{+6+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &4x & = &14\\\Leftrightarrow & \color{red}{4}x & = &14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-x } & = & -11 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+8}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-7x } & = & -3 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-15}& = & -8 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+6x } & = & -8 \color{red}{ -6x }\color{blue}{+15+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-9}& = & 2 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9+3x } & = & 2 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &10x & = &11\\\Leftrightarrow & \color{red}{10}x & = &11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+15}& = & -5 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-6x } & = & -5 \color{red}{ +6x }\color{blue}{-15-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &7x & = &-20\\\Leftrightarrow & \color{red}{7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)