Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-13}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-3x } & = & 15 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &-8x & = &28\\\Leftrightarrow & \color{red}{-8}x & = &28\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{28}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+6}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-9x } & = & -13 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &-22x & = &-19\\\Leftrightarrow & \color{red}{-22}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{-19}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{19}{22} } & & \\ & V = \left\{ \frac{19}{22} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+2}& = & 8 \color{red}{ +10x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-10x } & = & 8 \color{red}{ +10x }\color{blue}{-2-10x } \\\Leftrightarrow & -7x \color{blue}{-10x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &-17x & = &6\\\Leftrightarrow & \color{red}{-17}x & = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+14}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14+7x } & = & -13 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & -15x \color{blue}{+7x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-27\\\Leftrightarrow & \color{red}{-8}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-27}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{27}{8} } & & \\ & V = \left\{ \frac{27}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+10}& = & -9 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10+5x } & = & -9 \color{red}{ -5x }\color{blue}{-10+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &13x & = &-19\\\Leftrightarrow & \color{red}{13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+3}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3-13x } & = & -12 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-15\\\Leftrightarrow & \color{red}{-3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-x } & = & 9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &9x & = &18\\\Leftrightarrow & \color{red}{9}x & = &18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{18}{9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-8}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-14x } & = & -1 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &-27x & = &7\\\Leftrightarrow & \color{red}{-27}x & = &7\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{7}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{27} } & & \\ & V = \left\{ \frac{-7}{27} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+14}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-3x } & = & 2 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & -10x \color{blue}{-3x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-8}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x } & = & -12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-10}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10-3x } & = & -12 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+3}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3-4x } & = & 8 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 8 \color{blue}{-3} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)