Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-14}& = & 1 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14+5x } & = & 1 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-x } & = & -15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-27\\\Leftrightarrow & \color{red}{-11}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-27}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{27}{11} } & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+15}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15-11x } & = & 5 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+7}& = & -11 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7+3x } & = & -11 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &7x & = &-18\\\Leftrightarrow & \color{red}{7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+2}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-5x } & = & -9 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &-17x & = &-11\\\Leftrightarrow & \color{red}{-17}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-11}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-x } & = & -11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -11 \color{blue}{+10} \\\Leftrightarrow &5x & = &-1\\\Leftrightarrow & \color{red}{5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x } & = & 13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+2}& = & -6 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+3x } & = & -6 \color{red}{ -3x }\color{blue}{-2+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-x } & = & 15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{-14} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+14}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14-8x } & = & 10 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+9}& = & 13 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9-12x } & = & 13 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & 13 \color{blue}{-9} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+12}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-9x } & = & 14 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-17x & = &2\\\Leftrightarrow & \color{red}{-17}x & = &2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)